# AmitN

Brent@GMATPrepNow posted a reply to j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum
“Useful remainder property: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0 When j is divided by k, the remainder is m The above property ...”
Yesterday
Brent@GMATPrepNow posted a reply to Challenge question: Is positive integer p even? in the Data Sufficiency forum
“------ASIDE--------------------- Here''s a useful rule: If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors. Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors ...”
May 22, 2019
Brent@GMATPrepNow posted a new topic called j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum
“j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz? i) 49 ii) 50 iii) 56 A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii ...”
May 22, 2019
Brent@GMATPrepNow posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum
“One approach is to test values If n = 7, we get: (A) 7(7 + 1)(7 – 4) = (7)(8)(3). Definitely divisible by 3. KEEP (B) 7(7 + 2)(7 – 1) = (7)(9)(6). Definitely divisible by 3. KEEP (C) 7(7 + 3)(7 – 5) = (7)(10)(4). NOT divisible by 3. ELIMINATE. (D) 7(7 + 4)(7 – 2) = (7)(11)(5). NOT ...”
May 22, 2019
Brent@GMATPrepNow posted a reply to Question from mba.com mock test in the Problem Solving forum
“The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. So, 120 = 120 * 2^10)] + 60 Divide both sides by 60: 2 = 2 * 2^ f = 120 * 2^ The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit? f = 120 * 2^30)] + ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to OG #132 in the Problem Solving forum
“We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to ps 500 test27 #16 in the Problem Solving forum
“One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to problem to solve in the Problem Solving forum
“What we really have here is an algebra question requiring us to combine like terms. First, notice that K + K = 2K Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6 Similarly, notice that M + M + M = 3M Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6 So, 2^5 + ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to test 39 #13 in the Problem Solving forum
“Here''s a related question to practice with: https://www.beatthegmat.com/intensity-scale-readings-t273997.html Cheers, Brent”
May 21, 2019
Brent@GMATPrepNow posted a reply to test 38 #15 in the Problem Solving forum
“red = 7 yellow = 5 green = 3 blue = 2 147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7) So, there are 3 blue beads, 1 green bead, 3 yellow beads and 2 red beads. Cheers, Brent”
May 21, 2019
Brent@GMATPrepNow posted a reply to test35 # 15 in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Help on PS problem- GMATprep in the Problem Solving forum
“Let''s test the values using x = 0 So, we can reword the question as, For which of the following functions is f(0)=f(1-0) In other words, we''re looking for a function such that f(0) = f(1) A) f(x)=1-x f(0)=1-0 = 1 f(1)=1-1 = 0 Since f(0) doesn''t equal f(1), eliminate A B) f(x) = 1 - ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Probability in the Problem Solving forum
“We want: a) # of teams that include both John and Peter b) total # of 5-person teams possible a) # of teams that include both John and Peter Put John and Peter on the team (this can be accomplished in 1 way) Select the remaining 3 team-members from the remaining 7 players (this can be ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Mr. Jones spends $25 on movie tickets for a party of adults in the Data Sufficiency forum “ Given: Mr. Jones spends$25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost $3 each and children''s tickets cost$2 each. There are several scenarios that satisfy statement 1. Here are ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to A collection of 16 coins, each with a face value of either in the Problem Solving forum
“Let D = the NUMBER of 10-cent coins Let Q = the NUMBER of 25-cent coins Notice that the VALUE of Q 25-cent coins = ($0.25)Q For example, the VALUE of six 25-cent coins = ($0.25)6 = $1.50 And the VALUE of ten 25-cent coins = ($0.25)10 = $2.50 etc Likewise, the VALUE of D 10-cent coins = ...” May 21, 2019 Brent@GMATPrepNow posted a new topic called Challenge question: Is positive integer p even? in the Data Sufficiency forum “Is positive integer p even? (1) 4p has twice as many positive divisors as p has (2) 8p has 3 positive divisors more than p has Answer: A Source: www.gmatprepnow.com Difficulty level: 700+” May 20, 2019 Brent@GMATPrepNow posted a reply to In the figure above, if A, B, and C are the areas, respectiv in the Data Sufficiency forum “Key concept: We''re told that the area of the BLUE circle = the area of the RED circle https://i.imgur.com/AZaIFeU.png This means we can say: A + B = B + C Now onto the question..... Target question: What is the value of B + C ? Statement 1: A + 2B + C = 24 Rewrite this as: (A + B) ...” May 17, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency lesson #7: - The Table Method Video : https://www.youtube.com/watch?v=lYfTiRIG_k4 Cheers, Brent” May 16, 2019 Brent@GMATPrepNow posted a reply to If Mary always takes the same route to work, how long did it in the Data Sufficiency forum “Target question: How long did it take Mary to get to work on Friday? Statement 1: It took Mary 20 minutes to get to work on Thursday. Clearly, we cannot use this information to answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: Mary''s average speed ...” May 15, 2019 Brent@GMATPrepNow posted a reply to x-4=z y-x=8 8-z=t For the system of equations given, what in the Data Sufficiency forum “Target question: What is the value of z? Statement 1: x = 7 Scanning the three given equations, we see that equation i is all we need to determine the value of z i) x - 4 = z Replace x with 7 to get: 7 - 4 = z So, z = 3 Since we can answer the target question with certainty, statement 1 ...” May 14, 2019 Brent@GMATPrepNow posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum “KEY CONCEPT: 30-60-90 triangles are known as special right triangles, and we know quite a bit about this kind of triangle Target question: What is the length of segment JL ? Statement 1: JK = 10 https://i.imgur.com/sKEFT1R.png Compare ΔJKL with the BASE 30-60-90 triangle. Their ...” May 13, 2019 Brent@GMATPrepNow posted a reply to A line that passes through (–1, –4) and (3, k) has a slo in the Problem Solving forum “Slope of line between the points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1) So, we can write: k = [k - (-4)]/[3 - (-1)] Simplify: (k + 4)/4 = k Multiply both sides by 4 to get: k + 4 = 4k Subtract k from both sides to get: 4 = 3k Divide both sides by 3 to get: 4/3 = k Answer: C Cheers, ...” May 13, 2019 Brent@GMATPrepNow posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum “This question relies on our ability to determine the VALUE of any 2-digit number. For example, what is the VALUE of 83? For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just ...” May 13, 2019 Brent@GMATPrepNow posted a reply to If n is an integer greater than 10, then the expression (n^2 in the Problem Solving forum “-----ASIDE--------------------- There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be ...” May 12, 2019 Brent@GMATPrepNow posted a reply to If x and y are the lengths of the legs of a right triangle, in the Data Sufficiency forum “ Given: x and y are the lengths of the legs of a right triangle We have something like this: https://i.imgur.com/VxCexHO.png Target question: What is the value of xy? Statement 1: The hypotenuse of the triangle is There are infinitely-many different right triangles that meet this ...” May 11, 2019 Brent@GMATPrepNow posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum “Question rephrased: In how many different ways can we arrange the letters WWWLLD -------------ASIDE-------------------------------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the If there are n objects where A of them are ...” May 11, 2019 Brent@GMATPrepNow posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum “We can also solve the question using one variable Given: Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. Let G = the number of years Green worked at Firm X So, G - 4 = the number of years Smith worked at Firm X (since ...” May 10, 2019 Brent@GMATPrepNow posted a reply to In the below addition A, B, C, D, E, F, and G represent the in the Problem Solving forum “If we add two 2-digit numbers and the sum is a 3-digit number, then the 3-digit number must start with a 1. So, E = 1 In order for the sum to be a 3-digit number, A+C must be greater than 9 So, we have two options: EITHER A and C are 5 and 6, OR A and C are 4 and 6 If A and C are 5 and 6, ...” May 10, 2019 Brent@GMATPrepNow posted a reply to If xyz ≠ 0, what is the value of in the Data Sufficiency forum “Target question: What is the value of (x⁴z²)/(z²y²)? This is a good candidate for rephrasing the target question. Since z ≠ 0, we know that z² ≠ 0 So, we can safely take (x⁴z²)/(z²y²) and divide top and bottom by z² to get: x⁴/y² REPHRASED target question: What is the value ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Is quadrilateral PQRS a parallelogram? in the Data Sufficiency forum “Target question: Is quadrilateral PQRS a parallelogram? If you recognize that each statement on its own is not sufficient, we can jump straight to . . . Statements 1 and 2 combined There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two: Case a: PQRS could ...” May 9, 2019 Brent@GMATPrepNow posted a reply to A lecture course consists of 595 students. The students are in the Problem Solving forum “In order to have an EQUAL number of students in each section, the number of students per section MUST BE A FACTOR of 595 Let''s do some prime factorization 595 = (5)(7)(17) From the prime factorization, we can see that answer choice A, B, D and E are all factors of 595 Answer: C Cheers, ...” May 9, 2019 Brent@GMATPrepNow posted a reply to If a and b are constants, is the expression in the Data Sufficiency forum “Target question: Is the expression defined for x = –2? This is a great candidate for rephrasing the target question. If x = -2, then the expression becomes (-2)+b/√(-2+a) There are two ways in which the expression(-2)+b/√(-2+a) is NOT defined: case i) If a = 2, then the fraction''s ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Is x = y? in the Data Sufficiency forum “Target question: Is x = y? Statement 1: 2x/3 - y/3 = 1/3 Multiply both sides by 3 to get: 2x - y = 1 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, it is the case that x = y ...” May 9, 2019 Brent@GMATPrepNow posted a reply to The figure above represents a box that has the shape of a in the Data Sufficiency forum “Target question: What is the volume of the box? IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater ...” May 9, 2019 Brent@GMATPrepNow posted a reply to In the figure above, PQRT is a rectangle. What is the length in the Data Sufficiency forum “Let''s assign some variables to some of the lengths... https://i.imgur.com/BpaiRKm.png Target question: What is the value of x? Statement 1: The area of region PQRS is 39 and TS = 6. Region PQRS is a TRAPEZOID Area of trapezoid = (height)(base1 + base2)/2 So, we get: (x)(y + z)/2 = 39 ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico Ci in the Problem Solving forum “Here''s how I would answer this in my head Average speed = total distance/total time = 1200/2.5 = 2400/5 = 4800/10 = 480 Answer: D Cheers, Brent” May 9, 2019 Brent@GMATPrepNow posted a reply to What amount did Jean earn from the commission on her sales in the Data Sufficiency forum “Target question: What amount did Jean earn from the commission on her sales in the FIRST HALF of 1988 ? Statement 1: In 1988 Jean''s commission was 5 percent of the total amount of her sales. We don''t know her total sales amount in 1988, AND we don''t know what happened in the FIRST HALF of ...” May 8, 2019 Brent@GMATPrepNow posted a reply to Six shipments of machine parts were shipped from a factory o in the Data Sufficiency forum “We might be able to solve this one faster by first converting the fractions to decimals. S1=0.25 S2=0.2 S3=0.17 (approx) S4=0.15 S5=0.13 (approx) S6=0.1 Statement 1: S2 and S4 were shipped on the first truck. First truck has 0.2 + 0.15 = 0.35 Since the first truck holds more than 0.5, ...” May 7, 2019 Brent@GMATPrepNow posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum “\ Target question: Is a^5 > 4^b Statement 1: a³ = -27 Solve to get: a = -3 So, a^5 = (-3)^5 = -243 Since 4^b will be POSITIVE for all values of b, the answer to the target question is NO, a^5 is definitely NOT greater than 4^b Since we can answer the target question with certainty, ...” May 7, 2019 Brent@GMATPrepNow posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum “Let''s assume that we''re creating subcommittees. We want to place 6 people in the following spaces: _ _ _ | _ _ _ First, we place Michael in one subcommittee; it makes no difference which one: M _ _ | _ _ _ Now place Anthony. We can see that there are 5 spaces remaining. 2 spaces ...” May 7, 2019 Brent@GMATPrepNow posted a reply to If x is 8/3 percent of y, y is what percent of x? in the Problem Solving forum “x percent = x/100 So, 8/3 percent = (8/3)/100 = (8/3)/(100/1) = (8/3)(1/100) = 8/300 GIVEN: x is 8/3 percent of y, We can write: x = 8/300 of y In other words: x = (8/300)(y) or......: x = 8y/300 y is what percent of x? Take: x = 8y/300 Multiply both sides by 300 to get: 300x = 8y ...” May 7, 2019 Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum “A quick solution is to assign some values to the highest paid and lowest paid workers Let$10,000 = the lowest salary LAST YEAR Let $40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR =$30,000 If the annual salary of each of the 100 employees this ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum
“Hey BTGmoderatorDC, You posted this question 2 months ago: https://www.beatthegmat.com/last-year-the-range-of-the-annual-salaries-of-the-100-t306593.html Cheers, Brent”
May 4, 2019
Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum
“Approach #2: Algebra Let x = the width of the rectangle So, 2x = the length of the rectangle If the perimeter is 10, we can write: x + x + 2x + 2x = 10 Simplify: 6x = 10 Solve: x = 10/6 = 5/3 So, the width (x) is 5/3 And the length (2x) is 10/3 Answer: B Cheers, Brent”
May 4, 2019
Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum
“We COULD use algebra to solve this question. However, it''s probably faster to just test the answer choices The answer choices give us the length and width of the rectangle. So, the sum of two values will equal HALF the perimeter of the rectangle. Since we want a perimeter of 10, the ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Three-fourths of the area of a rectangular lawn 30 feet wide in the Problem Solving forum
“Here''s a diagram of the 30 x 40 lawn https://i.imgur.com/6dQyyQ5.png If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet https://i.imgur.com/nRkAVRU.png So, the enclosure is a 30 by 30 square. The PERIMETER = 30 + 30 + 30 + 30 = 120 feet If ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to If rectangle ABCD is inscribed in the circle above, what is in the Problem Solving forum
“Draw a line connecting points A and C. https://i.imgur.com/fQaxM5q.png An important circle property (see video below for more info) tells us that, if we have a 90-degree inscribed angle, then that angle must be containing ("holding") the DIAMETER of the circle. So, we know that AC = ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to In quadrilateral ABCD above, what is the length of AB ? in the Problem Solving forum
“https://i.imgur.com/srEvM6A.png If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem. https://i.imgur.com/L50lEKr.png Either way, we''ll see that the triangle''s ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to A paint mixture was formed by mixing exactly 3 colors of in the Data Sufficiency forum
“Target question: How many gallons of green paint were used? Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used. In other words, we ...”
May 2, 2019
Brent@GMATPrepNow posted a reply to If 2.00X and 3.00Y are 2 numbers in decimal form with thousa in the Data Sufficiency forum
“ Given: 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y Target question: Is 3(2.00X) > 2(3.00Y)? This is a good candidate for rephrasing the target question. Since X is the thousandths digit, we can write: 2.00X = 2 + X/1000 Since Y is the thousandths ...”
May 2, 2019
Brent@GMATPrepNow posted a reply to If n^m leaves a remainder of 1 after division by 7 for all in the Problem Solving forum
“The most important piece of information is here: "for all positive integers n that are not multiples of 7" Since 2 is not a multiple of 7, then it must be the case that, for a particular value of m, 2^m leaves a remainder of 1 after division by 7 Let''s check the answer choices.... ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to If x is an integer greater than 0, what is the remainder in the Data Sufficiency forum
“Target question: What is the remainder when x is divided by 4 ? Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What number is 6 more than x + y ? in the Data Sufficiency forum
“Target question: What is the value of x + y + 6? Statement 1: y is 3 less than x. We can write: y = x - 3 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Is the average (arithmetic mean) of the numbers x, y, and z in the Data Sufficiency forum
“Target question: Is the average (arithmetic mean) of the numbers x, y, and z greater than z? This is a good candidate for rephrasing the target question. Rewrite the question as "Is (x + y + z)/3 > z?" Multiply both sides by 3 to get: "Is x + y + z > 3z?" Subtract z ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum
“Target question: How many objects are in the box? Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green. We can solve this using the Double Matrix Method. This technique can be used for most questions featuring a population in which ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Target question: What is the remainder when the positive integer n is divided by 5 ? Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to Is n equal to zero? in the Data Sufficiency forum
“Target question: Is n equal to zero? Statement 1: The product of n and some nonzero number is 0 (n)(non-zero number) = 0 This means n must be 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The sum of n and 0 is 0 If n + 0 = 0, we can ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“ Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to How many hours does it take Jennifer to run y miles if she r in the Problem Solving forum
“time = distance/rate So, time = y/x Answer: B Cheers, Brent”
April 30, 2019
Brent@GMATPrepNow posted a reply to If x = 5 – 4k and y = 5k – 3, then for what value of k d in the Problem Solving forum
“We want: x = y Replace values with their equivalents: 5 - 4k = 5k - 3 Add 4k to both sides: 5 = 9k - 3 Add 3 to both sides: 8 = 9k Divide both sides by 9 to get: 8/9 = k Answer: B Cheers, Brent”
April 30, 2019
Brent@GMATPrepNow posted a reply to If a school district paid a total of $35 per desk for x desk in the Data Sufficiency forum “ Given: School district paid a total of$35 per desk for x desks and a total of $30 per table for y tables So, the TOTAL amount paid = 35x + 30y. Target question: What was the total amount that the district paid for these desks and tables?? Statement 1: The total amount the district ...” April 29, 2019 Brent@GMATPrepNow posted a reply to In a sequence of numbers in which each term is 2 more than in the Data Sufficiency forum “ Given: Sequence of numbers is such that each term is 2 more than the preceding term Target question: What is the value of term_4? Statement 1: The last term is 90. We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . . ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is the integer p divisible by 5 ? in the Data Sufficiency forum “Target question: Is the integer p divisible by 5? Statement 1: p is divisible by 10. If p is divisible by 10, we can write: p = 10k, for some integer k. Rewrite this as: p = (5)(2)(k) This tells us that p is a multiple of 5, which means p must be divisible by 5 Since we can answer the ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If R, S, and T are points on a line in the Data Sufficiency forum “ Given: R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S There are 4 possible scenarios that meet the above conditions: https://i.imgur.com/kOeqUfZ.png Target question: How far is S from T? Statement 1: R is between S and T. When we check the 4 ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum “ Given: m and n are integers Target question: What is the value of m + n ? Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0. Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn At this point, we ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum “ Given: a and b are integers, and b > 0 Target question: Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question. Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is the sum of two integers divisible by 10 ? in the Data Sufficiency forum “Target question: Is the sum of two integers divisible by 10 ? Statement 1: One of the integers is even. We only have information about ONE number. Statement 1 is NOT SUFFICIENT Statement 2: One of the integers is a multiple of 5. We only have information about ONE number. Statement 2 ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum “ Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers. Since p < r < s, we know that r = the mean = the median. In other ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Three children inherited a total of X dollars. If the oldest in the Data Sufficiency forum “ Given: Three children inherited a total of X dollars. The oldest child inherited$7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child Let y = the amount the YOUNGEST child received So, y + 7000 = the amount the OLDEST child received And y + ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is x<y? in the Data Sufficiency forum “Target question: Is x < y? Statement 1: z< y No information about x Statement 1 is NOT SUFFICIENT Statement 2: z < x No information about y Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined The combined statements tell us that x and y are both greater than z ...” April 28, 2019 Brent@GMATPrepNow posted a reply to What is the value of a^4 - b^4? in the Data Sufficiency forum “Target question: What is the value of a⁴ - b⁴? NOTE: a⁴ - b⁴ is a difference of square, which we can factor. a⁴ - b⁴ = (a² - b²)(a² + b²) So, we can REPHRASE the target question as... REPHRASED target question: What is the value of (a² - b²)(a² + b²)? Statement 1: ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Which of the following could be the equation of line m? in the Problem Solving forum “First off, we can eliminate answer choice D, since y = 2 is the equation of a HORIZONTAL line, and the given line is NOT horizontal. Next, we can eliminate answer choice E, since x = -2 is the equation of a VERTICAL line, and the given line is NOT vertical. Now notice that line m has a ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum “ Given: S is a set of odd integers and 3 and –1 are in S Target question: Is –15 in S ? Statement 1: 5 is in S So far, set S looks like this: {-1, 3, 5, . . . .} So, -15 may or may not be in set S Since we cannot answer the target question with certainty, statement 1 is NOT ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If r and s are positive integers... in the Data Sufficiency forum “ Given: r and s are positive integers Target question: Is r + s even? Statement 1: r is even. Since we have no information about s, we cannot determine whether r + s is even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: s is ...” April 28, 2019 Brent@GMATPrepNow posted a reply to When positive integer k is divided by 5, the remainder is 2. in the Problem Solving forum “When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Is the integer x a 3-digit integer? in the Data Sufficiency forum “Target question: Is the integer x a 3-digit integer? Statement 1: x is the square of an integer. Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 10² = 100. In this case, the answer to the target question is YES, x IS a 3-digit ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum “ Given: term1 = 0 and term2 = 1 Target question: Does term5 equal 2? Once we scan the two statements, we can probably jump straight to . . . Statements 1 and 2 combined There are several possible sequences that satisfy BOTH statements. Here are two: Case a: {0, 1, 2, 0, 2,...}. In ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum “Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is the sum of four particular integers even? Statement 1: Two of the integers are odd and two are even. ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If 90/k is an integer, is k an integer? in the Data Sufficiency forum “ Given: 90/k is an integer Target question: Is k an integer? Statement 1: k > 1 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 10. Notice that 90/k = 90/10 = 9, which is an integer. In this case, the answer to the target ...” April 27, 2019 Brent@GMATPrepNow posted a reply to For a recent play performance, the ticket prices were$25 in the Data Sufficiency forum
“Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled $10,500 In other ...” April 27, 2019 Brent@GMATPrepNow posted a reply to The arithmetic mean of a data set is 46 and the standard in the Problem Solving forum “-----------ASIDE----------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...” April 27, 2019 Brent@GMATPrepNow posted a reply to In the town of Z, the town lion roars on some days and not in the Data Sufficiency forum “Target question: What is the probability that on that day, either the town lion roared or it rained? This is a good candidate for rephrasing the target question. This is an OR probability. The OR probability rule says, P(A or B) = P(A) + P(B) - P(A and B) So, P(rained or roared) = P(rained) + ...” April 27, 2019 Brent@GMATPrepNow posted a reply to If 20 percent of x is 5y, and y = 7, what is 60 percent in the Problem Solving forum “GIVEN: 20 percent of x = 5y This means: 40 percent of x = 10y And: 60 percent of x = 15y Since y = 7, we can write: 60 percent of x = 15(7) = 105 Answer: A” April 27, 2019 Brent@GMATPrepNow posted a reply to Is x^2 > 15? in the Data Sufficiency forum “Target question: Is x² > 15? Statement 1: x > -4 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -1. In this case, x² = (-1)² = 1. So, the answer to the target question is NO, x² is NOT greater than 15 Case b: x = ...” April 27, 2019 Brent@GMATPrepNow posted a reply to If digit $$h$$ is the hudredths' digit in the decimal in the Data Sufficiency forum “ Given: Digit h is the hundredths digit in the decimal d=0.2h6 Target question: What is the value of d, rounded to the nearest TENTH? Statement 1: d < 1/4 In other words, 0.2h6 < 0.25 This means h = 0, 1, 2, 3 or 4 If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest ...” April 26, 2019 Brent@GMATPrepNow posted a reply to In the rectangular coordinate system, line $$k$$ is defined in the Data Sufficiency forum “KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line. Given: Line k is defined by the equation x - 2y + n = 0 Target question: What is the value of n? Statement 1: The x-intercept of line k is 8 In other words, ...” April 26, 2019 Brent@GMATPrepNow posted a reply to If z is a three-digit positive integer, what is the value in the Data Sufficiency forum “ Given: z is a three-digit positive integer Target question: What is the value of the tens digit of z ? Statement 1: The tens digit of z - 91 is 3 Let''s examine two EXTREME cases z - 91 = 30 z - 91 = 39 NOTE: These are extreme cases, because 30 is the smallest 2-digit number ...” April 25, 2019 Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, 2/3 are either pigs or in the Data Sufficiency forum “Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...” April 25, 2019 Brent@GMATPrepNow posted a reply to Bill rides his bike to work in the morning on a route that in the Data Sufficiency forum “Here''s a similar question to practice with: https://www.beatthegmat.com/distance-t273181.html Cheers, Brent” April 24, 2019 Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Statement 1: 4x = 2y − 6 Divide both sides by 2 to get: 2x = y - 3 Divide both sides by 2 (again) to get: x = (y - 3)/2 As you might guess, there are infinitely many solutions to the equation x = (y - 3)/2. Here are two: Case a: y = 3, and x = 0. ...” April 24, 2019 Brent@GMATPrepNow posted a reply to Phone plan A charges$1.25 for the first minute and $0.15 in the Problem Solving forum “Phone plan A charges$1.25 for the first minute and $0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call =$1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay $1.25 for the FIRST minute. So, if x = ...” April 24, 2019 Brent@GMATPrepNow posted a reply to A piece of twine of length t is cut into two pieces. in the Problem Solving forum “A piece of twine of length t is cut into two pieces. Let x = the length of the LONGER piece in yards So, t - x = the length of the SHORTER piece in yards The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. In other words: (longer piece) = ...” April 22, 2019 Brent@GMATPrepNow posted a reply to √(16∗20+8∗32)= in the Problem Solving forum “One option here is to evaluate (16)(20)+(8)(32), and then find the square root of the result. That''s a bit of work. We can also apply a technique called "Multiplying by Doubling and Halving" (here''s the video: I factored out the 16 = √sqrt(xy) = (√x)(√y)] √[(16)(36)] = ...” April 22, 2019 Brent@GMATPrepNow posted a reply to Sequence $$X$$ consists of $$825$$ terms, and each term in the Data Sufficiency forum “Target question: What is the value of term 500? Given: Each term after the first term is 5 more than the preceding term. Statement 1: Term 515 of sequence X is -98. Since each term is 5 more than the preceding term, we know that term 514 = -103 term 513 = -108 term 512 = -113 term ...” April 21, 2019 Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joon, Kendra, Lee, Marnie and in the Problem Solving forum “Our goal is to find P(M and N both selected) Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them is selected 1st) = 2/5 because I''m ...” April 21, 2019 Brent@GMATPrepNow posted a reply to What is the perimeter of quadrilateral Q? in the Data Sufficiency forum “Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...” April 20, 2019 Brent@GMATPrepNow posted a reply to Mary's income is 60 percent more than Tim's income, and in the Problem Solving forum “I suggest that we choose some nice values that meet the given conditions. Tim''s income is 40 percent less than Juan''s income. Let Juan''s income =$100 40% of $100 =$40 This means Tim''s income = $100 -$40 = $60 Mary''s income is 60 percent more than Tim''s income 60% of$60 = $36 So ...” April 20, 2019 Brent@GMATPrepNow posted a reply to For integers x and y, when x is divided by y, the remainder in the Problem Solving forum “Since, the question asks "Which of the following must be true?", we can eliminate any answer choice that is not necessarily true. So let''s test some values that satisfy the given conditions For integers x and y, when x is divided by y, the remainder is odd. One possible case is that ...” April 20, 2019 Brent@GMATPrepNow posted a reply to A certain library assesses fines for overdue books as follow in the Problem Solving forum “1st day -$0.10 2nd day - $0.20 or$0.40 (double or add $0.30)$0.20 is the lesser amount 3rd day - $0.40 or$0.50 (double or add $0.30)$0.40 is the lesser amount 4th day - $0.80 or$0.70 (double or add $0.30)$0.70 is the lesser amount The correct answer is B Cheers, Brent”
April 20, 2019
Brent@GMATPrepNow posted a reply to For the 5 days shown in the graph, how many kilowatt-hours in the Problem Solving forum
“List the numbers in ASCENDING ORDER to get: 19, 24, 27, 29, 31. So 27 is the median. Average = (19 + 24 + 27 + 29 + 31)/5 = 130/5 = 26. The median (27) is 1 greater than the average (26). Answer: A Cheers, Brent”
April 20, 2019
Brent@GMATPrepNow posted a reply to What are the coordinates of point B in the figure above? in the Data Sufficiency forum
“IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below. Target question: What ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to If (x # y) represents the remainder that results when the in the Problem Solving forum
“If y > 16, (16 # y) = 16, so we need only check the values from 1 to 15 Also, we need not check the FACTORS of 16, since they will all yield a remainder of 0 We''re left with: (16 # 3) = 1 KEEP! (16 # 5) = 1 KEEP (16 # 7) = 2 (16 # 9) = 7 (16 # 10) = 6 (16 # 11) = 5 (16 # 12) = 4 (16 # ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers, is x^2*y^2 even ? in the Data Sufficiency forum
“Target question: Is x²y² even ? Statement 1: x + 5 is a prime number So, x+5 is a prime number greater than 5, which means x+5 must be ODD (since 2 is only even prime) If x+5 is ODD, then x must be EVEN If x is EVEN, then x²y² must be even The answer to the target question is YES, ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to The areas of three faces of a rectangular solid are 12, 15 a in the Problem Solving forum
“Let x = the width Let y = the length Let z = the height So, the volume = xyz Area of one face = 12 We can write: xy = 12 Area of one face = 15 We can write: xz = 15 Area of one face = 20 We can write: yz = 20 Combine to get: (xy)(xz)(yz) = (12)(15)(20) Simplify: x²y²z² = 3600 ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum
“The OGs vary by very little with each edition. So, you can just use an earlier edition (see https://www.beatthegmat.com/official-guide-question-library-t296759.html) Cheers, Brent”
April 18, 2019
Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum
“Sorry, but there are no plans to update BTG''s 60-Day Study Guide to include OG2019 questions.”
April 18, 2019
Brent@GMATPrepNow posted a reply to If f(2x - 1) = 4x² - 4x - 8, then f(5) = in the Problem Solving forum
“Here''s one more approach: First notice that 4x² - 4x - 8 looks a lot like (2x - 1)² (2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1 Now take: f(2x - 1) = 4x² - 4x - 8 Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9 In other words, f(something) =something² - 9 In general, ...”
April 18, 2019
Brent@GMATPrepNow posted a reply to y = 248 - 398x. Which of the following values of x gives in the Problem Solving forum
“We can also test the answer choices.... (A) x = 200 means y = 248 - 398(200) = some number LESS THAN 248 (B) x = 100 means y = 248 - 398(100) = some number LESS THAN 248 (C) x = 0.5 means y = 248 - 398(0.5) = some number LESS THAN 248 (D) x = 0 means y = 248 - 398(0) = some number EQUAL TO ...”
April 18, 2019
Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum
“Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...”
April 18, 2019
Brent@GMATPrepNow posted a reply to Does x + c = y + c ? in the Data Sufficiency forum
“Target question: Does x + c = y + c ? This is a good candidate for rephrasing the target question. Take the equation x + c = y + c, and subtract c from both sides to get: x = y REPHRASED target question: Does x = y ? Aside: Here’s a video with tips on rephrasing the target question: ...”
April 17, 2019
Brent@GMATPrepNow posted a reply to If n is a prime number greater than 3, what is the remainder in the Problem Solving forum
“Choose ANY prime number greater than 3, and test it. If n = 5, then n² = 5² = 25 When 25 is divided by 12, the quotient is 2 and the remainder is 1 Answer: B Cheers, Brent”
April 17, 2019
Brent@GMATPrepNow posted a reply to Is integer x odd? in the Data Sufficiency forum
“Target question: Is integer x odd? Statement 1: 2x + 1 is odd There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. Notice that 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, the answer to the target question is YES, x IS odd Case b: x = 2. Notice that 2x ...”
April 17, 2019
Brent@GMATPrepNow posted a reply to When 1,000 children were inoculated with a certain vaccine, in the Data Sufficiency forum
“Target question: How many of the children developed inflammation but not fever? One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). ...”
April 16, 2019
Brent@GMATPrepNow posted a reply to Is xy > 0? in the Data Sufficiency forum
“Target question: Is xy > 0? Statement 1: x - y > -2 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is YES, xy IS greater than 0 Case b: ...”
April 16, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers and x = 10y + 5, what is in the Problem Solving forum
“GIVEN: x = 10y + 5 Factor out 5 to get: x = 5(2y + 1) We can see that x is a multiple of 5, which also means x is divisible by 5, which means the remainder will by ZERO when x is divided by 5 Answer: A Cheers, Brent”
April 16, 2019
Brent@GMATPrepNow posted a reply to Last Problem in OG12 Diagnostic in the Problem Solving forum
“As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach. Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier. However, the algebraic ...”
April 16, 2019
Brent@GMATPrepNow posted a reply to Which of the following is equivalent to in the Problem Solving forum
“Here''s another approach.... Take: $$\frac{x+y}{3}-\frac{x-y}{4}$$ Find common denominator: $$\frac{4(x+y)}{12}-\frac{3(x-y)}{12}$$ Expand numerators: $$\frac{4x+4y}{12}-\frac{3x-3y)}{12}$$ Combine fractions: $$\frac{(4x+4y)-(3x-3y)}{12}$$ Simplify numerator: $$\frac{x+7y}{12}$$ ...”
April 15, 2019
Brent@GMATPrepNow posted a reply to A man spends $48 to buy 6 hamburgers and 8 colas for his in the Problem Solving forum “Let H = price of one hamburger Let C = price of one cola A man spends$48 to buy 6 hamburgers and 8 colas for his office workers. 6H + 8C = 48 The next day, he buys 5 hamburgers and 4 colas and spends $32. 5H + 4C = 32 Assuming the prices of hamburgers and colas remain constant, what ...” April 15, 2019 Brent@GMATPrepNow posted a reply to Alice, Benjamin, and Carol each try independently to win a in the Problem Solving forum “P(exactly 2 win) = P(A wins and B wins and C loses OR B wins and C wins and A loses OR A wins and C wins and B loses) = P(A wins and B wins and C loses) + P(B wins and C wins and A loses) + P(A wins and C wins and B loses) Let''s calculate each probability P(A wins and B wins and C loses) = ...” April 15, 2019 Brent@GMATPrepNow posted a reply to If n is an integer, is (100−n)n an integer? in the Data Sufficiency forum “Target question: Is (100 - n)/n an integer? Statement 1: n > 4 Let''s TEST some values There are infinitely many values of n that satisfy statement 1. Here are two: Case a: n = 5. In this case, (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - ...” April 14, 2019 Brent@GMATPrepNow posted a reply to f(x) = x^2 - x. For which of the following values of a is in the Problem Solving forum “GIVEN: f(x) = x² - x So, f(8) = 8² - 8 = 56 I. a = -7 So, f(-7) = (-7)² - (-7) = 56 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE B and C II. a = -8 So, f(-8) = (-8)² - (-8) = 72 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE A II. a = -9 ...” April 14, 2019 Brent@GMATPrepNow posted a reply to What is the largest value of integer n such that in the Problem Solving forum “98 = (2)(7)(7) = (2^1)(7^2) So, 98^98 = (2^1)(7^2)]^98 = (2^98)(7^196) What is the largest value of integer n such that 98^98 is divisible by 7^n? Since 98^98 = (2^98)(7^196), the largest value of n is 196 Answer: E Cheers, Brent” April 14, 2019 Brent@GMATPrepNow posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum “I''m not crazy about this question. Typically, when we talk about series, Sn represents the SUM of the first n terms of that series. However, based on the official answer, Sn seems to represent the value of TERM n. Cheers, Brent” April 12, 2019 e-GMAT posted a reply to GMAT Quantitative: Question of the Week in the GMAT Math forum “Hello all, We have added a new question this week in our Question of the Week series. Give it a try. Question of the Week- 4 Also, try the previous problems of this series, if you have not done it yet. Stay tuned for more questions. Happy learning. :) Regards,” April 12, 2019 e-GMAT posted a new topic called e-GMAT Question of the Week #4 in the Problem Solving forum “While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time ...” April 12, 2019 Brent@GMATPrepNow posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum “To get a better idea of what''s happening, let''s sketch the set-up: https://i.imgur.com/SwHzFJD.png Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time. ...” April 11, 2019 e-GMAT posted a reply to GMAT Quantitative: Question of the Week in the GMAT Math forum “Hello all, We have posted the Official Solution of the Question of the Week #3 Happy learning. :) Regards,” April 11, 2019 e-GMAT posted a reply to Question of the Week - 3 (The value of the variable E is...) in the Problem Solving forum “Solution Given: In this question, we are given that • The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. To find: We need to determine • Among the given options, which one can be a possible value of the reciprocal of E. Approach ...” April 11, 2019 Brent@GMATPrepNow posted a reply to What is the sum of the cubes of the first ten positive? in the Problem Solving forum “Let''s look for a pattern 1³ = 1 = 1² 1³ + 2³ = 9 = 3² 1³ + 2³ + 3³ = 36 = 6² 1³ + 2³ + 3³ + 4³ = 100 = 10² 1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15² See the pattern yet? 1 + 2 = 3 3 + 3 = 6 6 + 4 = 10 10 + 5 = 15 First we add 2, then we add 3, then 4, then 5, etc ...” April 11, 2019 Brent@GMATPrepNow posted a reply to If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the in the Problem Solving forum “We need to examine powers of 10 that are smaller than AND greater than 0.00012345 We know that: 0.0001 < 0.00012345 < 0.001 Rewrite as FRACTIONS to get: 1/10,000 < 0.00012345 < 1/1,000 Rewrite as POWERS OF 10 to get: 1/10⁴ < 0.00012345 < 1/10³ We''re told that 0.00012345 ...” April 10, 2019 Brent@GMATPrepNow posted a reply to GMAT Prep Practice Test Quant Questions #4 in the GMAT Math forum “ Given: wx = y Target question: What is the value of xy ? Statement 1: wx²= 16 We can rewrite this as: (wx)(x) = 16 Since wx = y, we can replace wx with y to get: (y)(x) = 16 So, the answer to the target question is xy = 16 Since we can answer the target question with certainty, ...” April 9, 2019 Brent@GMATPrepNow posted a reply to A camera lens filter kit containing 5 filters sells for$ in the Problem Solving forum
“2 of them are priced at $10.45 each, 2 at$12.05 each, 1 at $17.50 TOTAL cost when purchased individually = (2 x$10.45) + (2 x $12.05) + (1 x$17.50) = $20.90 +$24.10 + $17.50 =$62.50 The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased ...”
April 9, 2019
Brent@GMATPrepNow posted a reply to Machine A produces pencils at a constant rate of 9000 in the Problem Solving forum
“To MINIMIZE machine B''s operating time, we must MAXIMIZE the time machine A''s operating time. So, let machine A operate for the full 8 hours. In 8 hours, machine A produces 72,000 pencils So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000 Time = output/rate So, ...”
April 9, 2019
Brent@GMATPrepNow posted a reply to Any decimal that has only a finite number of nonzero digits in the Data Sufficiency forum
“Target question: Is r/s a terminating decimal? Statement 1: 90 < r < 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal Case b: r = 91 and s = 3, in which case r/s = 91/3 = ...”
April 8, 2019
Brent@GMATPrepNow posted a reply to A sewing store buys fabric X by the bolt at the wholesale in the Data Sufficiency forum
“Target question: What is the wholesale price of a bolt of fabric X? Given: Each bolt contains 50 meters of fabric X Statement 1: The store sells fabric X for $6.25 per meter. No information about the relationship between the WHOLESALE price and the RETAIL price Statement 1 is NOT ...” April 8, 2019 Brent@GMATPrepNow posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish in the Problem Solving forum “Let''s use the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P( 2 different languages) = 1 - P(NOT 2 different languages) So, we can write: P(2 different languages) = 1 - P(the 2 languages are the SAME) P(the 2 languages are the SAME) P(the 2 ...” April 8, 2019 Brent@GMATPrepNow posted a reply to Any feedback on the Orion GMAT prep? in the Helpful Resources forum “Sorry - I know almost nothing about that company. Cheers, Brent” April 7, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency lesson #6: - Rephrasing the Target Question Video : https://www.youtube.com/watch?v=MyG1K3ee69w Cheers, Brent” April 7, 2019 Brent@GMATPrepNow posted a reply to In a certain game only one player can win and only one in the Data Sufficiency forum “Target question: What is the probability that Katelyn wins at least one of the 3 games? This is a good candidate for rephrasing the target question. In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game. We ...” April 7, 2019 Brent@GMATPrepNow posted a reply to Question of the Week - 3 (The value of the variable E is...) in the Problem Solving forum “A fast approach is to use some estimation. E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 ≈ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05 ≈1.4 Which of the following can be a possible value of the reciprocal of E? The reciprocal of E ...” April 7, 2019 e-GMAT posted a reply to GMAT Quantitative: Question of the Week in the GMAT Math forum “Hello all, We have added a new question this week in our Question of the Week series. Give it a try. Question of the Week- 3 Also, try the previous problems of this series, if you have not done it yet. Stay tuned for more questions. Happy learning. :) Regards,” April 7, 2019 e-GMAT posted a new topic called Question of the Week - 2 (The value of the variable E is...) in the Problem Solving forum “The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. Which of the following can be a possible value of the reciprocal of E? A. 0.154 B. 0.1818 C. 0.667 D. 2 E. 3.03 To access all questions: Consolidated list of Questions of the Week” April 7, 2019 Brent@GMATPrepNow posted a reply to Is the positive integer x an even number? in the Data Sufficiency forum “OA=E Target question: Is x an even number? Jump straight to..... Statements 1 and 2 combined There are infinitely many values of x that satisfy BOTH statements. Here are two: Case a: x = 32. In this case, the answer to the target question is YES, x IS an even number Case b: x = 17. ...” April 6, 2019 Brent@GMATPrepNow posted a reply to During a trip that they took together, Carmen, Juan, Maria, in the Problem Solving forum “Let x = the number of miles Rafael drove Average = 80 So, (72 + 78 + 83 + x)/4 = 80 Multiply both sides by 4 to get: 72 + 78 + 83 + x = 320 Simplify: 233 + x = 320 Solve: x = 87 Answer: D” April 6, 2019 Brent@GMATPrepNow posted a reply to If a certain animated cartoon consists of a total of 17,280 in the Data Sufficiency forum “Target question: How many minutes will it take to run the cartoon? Given: cartoon consists of a total of 17,280 frames Statement 1: The cartoon runs without interruption at the rate of 24 frames per second. Time = (output)/(rate) So, time = (17,280 frames)/(24 frames per second) NOTE: ...” April 6, 2019 Brent@GMATPrepNow posted a reply to While a family was away on vacation, they paid in the Problem Solving forum “..... paid a neighborhood boy$11 per week to mow their lawn... So, in 3 weeks, the amount the family paid for lawn-moving = (3 weeks)($11/week) =$33 ...the family paid $4 per DAY to feed and walk their dog... 3 weeks = 21 DAYS So, the amount the family paid for dog care = (21 days)($4/day) = ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to Last year $48,000 of a certain store's profit was shared in the Problem Solving forum “Each owner received 3 times as much as each employee Let E = the amount (in dollars) that ONE employee received So, 3E = the amount (in dollars) that ONE owner received Last year$48,000 of a certain store''s profit was shared by its 2 owners and their 10 employees. In other words: 3E + 3E + ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to Alice is twice as old as Brian and Cathy is 6 years in the Problem Solving forum
“GIVEN: Alice is a years old Alice is twice as old as Brian This also means Brian is HALF as old as Alice So, Brian''s age = a/2 Cathy is 6 years younger than Brian So, Cathy''s age = (Brian''s age) - 6 So, Cathy''s age = (a/2) - 6 How old is Cathy in terms of a ? Cathy''s age = (a/2) - ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to For all numbers m and n... in the Problem Solving forum
“GOAL: Find the value of 4?3 GIVEN: m?n = (2m - n)(m+ n) So, 4?3 = (2(4) - 3)(4+ 3) = (5)(7) = 35 Answer: A Cheers, Brent”
April 6, 2019
Brent@GMATPrepNow posted a reply to If x and y are two points on the number line what is the in the Data Sufficiency forum
“Target question: What is the value of x + y? Statement 1: 6 is halfway between x and y. KEY CONCEPT: The average (arithmetic mean) of 2 numbers is HALFWAY between those 2 numbers. For example, the average of 1 and 9 is 5. Notice that 5 is HALFWAY between 1 and 9. So, statement is ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to The residents of Town X participated in a survey to in the Problem Solving forum
“---------ASIDE-------------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In the xy-coordinate system, line k has slope 1/2 and passes in the Problem Solving forum
“Let''s first determine the equation of line k A quick approach is the write the equation of line k in slope y-intercept form: y = mx + b, where m = slope and b = y-intercept. We''re told that the slope = 0.5 and the point (0,5) tells us that the y-intercept is 5 So, the equation of line k is: ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum
“Another approach: Let M = number of men CURRENTLY in the office Let W = number of women CURRENTLY in the office In a certain office, the ratio of men to women is CURRENTLY 3/4. We can write: M/W = 3/4 Cross multiply to get: 4M = 3W Rewrite as: 4M - 3W = 0 If 10 men were added to the ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum
“In a certain office, the ratio of men to women is 3/4. This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women. It also tells us that the TOTAL number of men and women currently in the office is divisible by 7 When we check the answer choices, we see that A, B and E ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In the diagram above, points A, B, C, D, and E represent the in the Problem Solving forum
“points A, B, C, D, and E represent the five teams in a certain league in which each team must play each of the other teams exactly once. Let''s first determine the total number of games that will be played. There are 5 teams, so each team will play 4 games (since a team can''t play itself) So, ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to John and Mary were each paid x dollars in advance to do a in the Problem Solving forum
“One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to On a certain sightseeing tour, the ratio of the number in the Data Sufficiency forum
“Let W = # of women Let M = # of men Let C = # of children Target question: What is the value of M? Given: The ratio of the number of women to the number of children was 5 to 2 In other words, W : C = 5 : 2 Statement 1: On the sight-seeing tour, the ratio of the number of children to ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to Five friends - Ross, Phoebe, Chandler, Joey, and Monica in the Problem Solving forum
“Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to The y intercept of a line L is 4. If the slope of L is in the Problem Solving forum
“Let''s draw a bunch of lines with a negative slope AND have a y-intercept of 4 (ie, passes through the point (0,4)) We get: http://i1168.photobucket.com/albums/r500/GMATPrepNow/x-int_zpsswbinqns.png As we can see, the x-intercept can have ANY POSITIVE value. So, the x-intercept COULD be 6, ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to In the rectangular solid above, if each dimession of the in the Data Sufficiency forum
“Here''s a very similar (official) practice question: https://www.beatthegmat.com/volume-of-rectangular-solid-t273956.html Cheers, Brent”
April 5, 2019
Brent@GMATPrepNow posted a reply to Is x < 0? in the Data Sufficiency forum
“Target question: Is x < 0? Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to In the sequence S, each term after the first is twice the in the Problem Solving forum
“term1 = 3 term2 = (3)(2) = (3)(2¹) term3 = (3)(2)(2) = (3)(2²) term4 = (3)(2)(2)(2) = (3)(2³) term5 = (3)(2)(2)(2)(2) = (3)(2⁴) . . term14 = (3)(2^13) term15 = (3)(2^14) term16 = (3)(2^15) What is the sum of the 14th, 15th, and 16th terms in sequence S? Sum = (3)(2^13) + ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to If x, y, and d are integers and d is odd, are both x and y in the Data Sufficiency forum
“ Given: x, y, and d are integers and d is odd Target question: Are both x and y divisible by d? Statement 1: x+y is divisible by d. Let''s TEST some values. There are several values of x, y and d that satisfy statement 1. Here are two: Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = ...”
April 4, 2019
Brent@GMATPrepNow posted a reply to m and n are positive integers. Are m and n consecutive integ in the Data Sufficiency forum
“ Given: m and n are positive integers. Target question: Are m and n consecutive integers? Statement 1: m² + n² = 5 Since m and n are positive integers, there are only two possible solutions: Solution #1: m = 1 and n = 2 Solution #2: m = 2 and n = 1 In BOTH possible cases, the ...”
April 3, 2019
e-GMAT posted a reply to GMAT Quantitative: Question of the Week in the GMAT Math forum
“Hello all, We have posted the Official Solution of the Question of the Week #1 and Question of the Week - 2 Happy learning. :) Regards,”
April 3, 2019
e-GMAT posted a reply to Question of the Week - 2 (If x and y are non-zero integers ) in the Problem Solving forum
“Solution Given: In this question, we are given that • The numbers x and y are non-zero integers. • Also, |x – 3| ≤ 2 and -1 ≤ y ≤ 8. To find: We need to determine • The least value of x/y lies in which of the given ranges. Approach and Working: For the non-zero integer ...”
April 3, 2019
Brent@GMATPrepNow posted a reply to If Norbert can cut up one plastic six pack container in 30 in the Problem Solving forum
“We can solve this question by applying equivalent ratios For every 30 seconds that elapse, Norbert can cut up 1 plastic six-pack container In other words, for every 0.5 MINUTES that elapse, Norbert can cut up 1 plastic six-pack container Let t = the time (in MINUTES) to cut up 512 plastic ...”
April 2, 2019
Brent@GMATPrepNow posted a reply to For what percent of those tested for a certain infection was in the Data Sufficiency forum
“I just want to point out that Jay has done a perfect job employing a technique known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of patients, and the ...”
April 2, 2019
Brent@GMATPrepNow posted a reply to What is the number of cans that can be packed in a certain in the Data Sufficiency forum
“Target question: What is the number of cans that can be packed in a certain carton? Let''s head straight to..... Statements 1 and 2 combined Consider these two conflicting cases (that satisfy BOTH statements): Case a: the dimensions of the box are numbers are 1 x 1 x 2304 (inches), in ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=? in the Problem Solving forum
“Let''s look for a pattern... We want: 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? 2 + 2 + 2^2 = 4 + 4 = 8 = 2^3 So, 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 2^3 + 2^3 = 2(2^3) = 2^4 So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^4 + ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If n is the smallest of three consecutive positive integers in the Problem Solving forum
“There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to A collection of 36 cards consists of 4 sets of 9 cards in the Data Sufficiency forum
“Target question: What is the number on the card? Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6. 1+2+3+4+5+6+7+8+9=45 Since there are 4 sets of ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If x = 1 – 2y, what is z? in the Data Sufficiency forum
“Target question: What is the value of z? Given: x = 1 – 2y Statement 1: 5x + 10y + z = 5 Replace x with 1 – 2y to get: 5(1 – 2y) + 10y + z = 5 Expand: 5 - 10y + 10y + z = 5 Simplify: 5 + z = 5 Solve: z = 0 Since we can answer the target question with certainty, statement 1 is ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to Is x > 0? in the Data Sufficiency forum
“Target question: Is x > 0? Statement 1: x² > 0 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. In this case, the answer to the target question is YES, it is the case that x > ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If y is the smallest positive integer such that 3,150 in the Problem Solving forum
“Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5) Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If 3 less than twice a certain number is equal to 2 more in the Problem Solving forum
“Let x be the number 3 less than twice a certain number is equal to 2 more than 3 times the number We can write: 2x - 3 = 3x + 2 So: -3 = x + 2 Solve: -5 = x 5 less than 5 times the number is 5 times the number = 5(-5) = -25 So, 5 less than 5 times the number = -25 - 5 = -30 Answer: A ...”
March 31, 2019
Brent@GMATPrepNow posted a reply to Which of the following inequalities is an algebraic in the Problem Solving forum
“When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Note: these rules assume that k is positive (A) |x| ≤ 3 ...”
March 31, 2019
e-GMAT posted a new topic called Question of the Week - 2 (If x and y are non-zero integers ) in the Problem Solving forum
“If x and y are non-zero integers and |x – 3| ≤ 2 and -1 ≤ y ≤ 8 then the least value of x/y lies in which of the following range? A. Between -5.5 and -4.5 B. Between -4.5 and -3.5 C. Between -3.5 and -2.5 D. Between -2.5 and -1 E. Greater than -1”
March 30, 2019
e-GMAT posted a reply to e-GMAT Question of the Week #1 in the Problem Solving forum
“Solution Given: The number n is the product of the first 49 natural numbers The numbers $$\frac{n}{24^p}$$ and $$\frac{n}{36^q}$$ are integers To find: The maximum possible value of p + q Approach and Working: When it is given that $$\frac{n}{24^p}$$ is an integer, it necessarily means p ...”
March 30, 2019
Brent@GMATPrepNow posted a reply to In how many ways a criket team consisting of 5 batsmen, 4 in the Problem Solving forum
“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to What percentage of his bills did Stanley pay before their in the Data Sufficiency forum
“Target question: What percentage of his bills did Stanley pay before their due dates last month? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: Let P = # of bills PAID before due date Let T = TOTAL # of ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to If $$n$$ is a positive integer and $$r$$ is the remainder in the Data Sufficiency forum
“ Given: r is the remainder when (n² - 1) is divided by 8 Target question: What is the value of r? Statement 1: n is odd Let''s test some ODD values of n If n = 1, then n² - 1 = 1² - 1 = 0, and 0 divided by 8 leaves remainder 0. So, the answer to the target question is r = 0 If n = 3, ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum
“ Given: √k is not an integer Target question: Is k a prime number? Statement 1: k < 10 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to The ratio of boys to girls in Class A is 3 to 4. The ratio in the Problem Solving forum
“The ratio of boys to girls in Class A is 3 to 4. Let B = number of boys in class A Let G = number of girls in class A We get: B/G = 3/4 Cross multiply to get: 4B = 3G Class A has one more boy and two more girls than class B So B - 1 = number of boys in class B So G - 2 = number of girls in ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #5: - Summarizing Information Video : https://www.youtube.com/watch?v=cK9PR3SLsSA Cheers, Brent”
March 27, 2019
Brent@GMATPrepNow posted a reply to The water from one outlet, flowing at a constant rate, can in the Problem Solving forum
“So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours So, this outlet pumps at a rate of 5 gallons per hour The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 ...”
March 27, 2019
Brent@GMATPrepNow posted a reply to If a positive integer t is not divisible by 5, how many poss in the Problem Solving forum
“Since t is NOT divisible by 5, we need only test t = 1, 2, 3 and 4 If t = 1, then t⁴ = 1, and 1 divided by 5 leaves remainder 1 If t = 2, then t⁴ = 16, and 16 divided by 5 leaves remainder 1 If t = 3, then t⁴ = 81, and 81 divided by 5 leaves remainder 1 If t = 4, then t⁴ = 256, and ...”
March 27, 2019
Brent@GMATPrepNow posted a reply to At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum
“There''s a nice integer properties rule that says: If j is a multiple of d, and k is NOT a multiple of d, then j-k (and j+k) is NOT a multiple of d For example, since 56 is a multiple of 7, and 11 is NOT a multiple of 7, then 56-11 is NOT a multiple of 7 At a certain school, the student to ...”
March 27, 2019
Brent@GMATPrepNow posted a new topic called At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum
“At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 ...”
March 26, 2019
Brent@GMATPrepNow posted a reply to For all positive integers m in the Problem Solving forum
“Thanks Roach! Cheers, Brent - now with 50% less "t"!!”
March 25, 2019
Brent@GMATPrepNow posted a reply to When f(x)=x^3+1/x3, which of the following is equal to f(-1/ in the Problem Solving forum
“GIVEN: f(x)=x³ + 1/x³ So, f(-1/x) = (-1/x)³ + 1/(-1/x)³ = -1/x³ + 1/(-1/x³) = -1/x³ - x³ = -(1/x³ + x³) = -(x³ + 1/x³) = -f(x) Answer: B Cheers, Brent”
March 25, 2019
Brent@GMATPrepNow posted a reply to Last year a certain bond with a face value of $5,000 yielded in the Problem Solving forum “Last year a certain bond with a face value of$5,000 yielded 8 percent of its face value in interest 8% of $5,000 =$400 So, interest = $400 If that interest was approximately 6.5 percent of the bond''s selling price,approximately what was the bond''s selling price? Let x = the bond''s ...” March 25, 2019 Brent@GMATPrepNow posted a reply to Is it true that x > 0? in the Data Sufficiency forum “Target question: Is it true that x > 0? Statement 1: x² = 2x Rewrite as: x² - 2x = 0 Factor: x(x - 2) = 0 So, EITHER x = 0 OR x = 2 Let''s examine each possible case Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0 Case b: If x = 2, then ...” March 24, 2019 Brent@GMATPrepNow posted a reply to Problem with a practice question in the GMAT Math forum “Here''s my full solution: https://www.beatthegmat.com/for-all-positive-integers-m-t299496.html Cheers, Brent” March 23, 2019 Brent@GMATPrepNow posted a reply to If $$xy \neq 0$$, and 75 percent of $$x$$ equals 125 percent in the Problem Solving forum “GIVEN: 75 percent of x equals 125 percent of y Rewrite as: 3/4 of x = 5/4 of y Or we can say: (3/4)(x) = (5/4)( y) Multiply both sides by 4 to get: 3x = 5y Divide both sides by 5 to get: 3x/5 = y Rewrite as: y = (3/5)(x) Or y = 3/5 of x Or y = 60/100 of x Or y = 60% of x Answer: C ...” March 22, 2019 Brent@GMATPrepNow posted a reply to If m and n are prime numbers, what is the value of m+n? in the Data Sufficiency forum “ Given: m and n are prime numbers Target question: What is the value of m+n? Statement 1: 15 ≤ m < n ≤ 20 17 and 19 are the only PRIME numbers from 15 to 20 inclusive So, it must be the case that m = 17 and n = 19 So, the answer to the target question is m+n = 17 + 19 = 33 Since ...” March 22, 2019 Brent@GMATPrepNow posted a reply to If n is an integer, is n + 1 odd? in the Data Sufficiency forum “Target question: Is n + 1 odd? Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN Statement 1: n + 2 is an even integer. In other words: n + EVEN = EVEN In other words: n = EVEN - EVEN By Rule #3, n must be even, which means n+1 is ODD The ...” March 22, 2019 Brent@GMATPrepNow posted a reply to Express 2^20-2^19-2^18-2^17 as a power of 2. in the Problem Solving forum “2^20 - 2^19 - 2^18 - 2^17 = 2^17(2^3 - 2^2 - 2^1 - 1) = 2^17(8 - 4 - 2 - 1) = 2^17(1) = 2^17 Answer: C Cheers, Brent” March 22, 2019 Brent@GMATPrepNow posted a reply to What is the total cost to make 7 long distance telephone in the Data Sufficiency forum “Target question: What is the total cost to make 7 long distance telephone calls? When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: ...” March 21, 2019 Brent@GMATPrepNow posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill in the Problem Solving forum “The ride up the mountain took 135 seconds longer than her run down the mountain Start with a word equation: (time going UP mountain) = (time going DOWN mountain) + 135 time = distance/speed We can now write: 300/(x - 8) = 300/(x + 10) + 135 Multiply both sides by (x - 8) to get: 300 = 300(x - ...” March 21, 2019 Brent@GMATPrepNow posted a reply to x is the product of all even numbers from 2 to 50, inclusive in the Problem Solving forum “x = (2)(4)(6)....(46)(48)(50) = (1)(2)(2)(2)(3)(2).....(23)(2)(24)(2)(25)(2) Notice that: x is divisible by 2. This tells us that x+1 is 1 greater than a multiple of 2. In other words, x+1 is NOT divisible by 2 x is divisible by 3. This tells us that x+1 is 1 greater than a multiple of 3. ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum “Here''s one approach. Take the task of selecting the 3 committee members and break it into stages. Stage 1: Select the 3 twins from which we will select 1 spouse each. There are 4 sets of twins, and we must select 3 of them. Since the order in which we select the 3 twins does not matter, ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If arc PQR above is a semicircle, what is the length of diam in the Data Sufficiency forum “http://s16.postimg.cc/p2mwbwdpt/triangle_PQR.jpg We can answer this question without performing any calculations. Instead, we can use some visualization. Important point: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or ...” March 20, 2019 Brent@GMATPrepNow posted a reply to In a group of children, the average (arithmetic mean) weight in the Problem Solving forum “We can also use weighted averages to solve this Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let G = number of girls Let B = number of boys So, G+B = TOTAL number of children ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of five consecutive negativ in the Problem Solving forum “Let x = the 1st (smallest integer) So, x+1 = the 2nd integer x+2 = the 3rd integer x+3 = the 4th integer x+4 = the 5th integer (greatest integer) What is the difference between the greatest and least of the five integers? Difference = ( x+4) - x = 4 Answer: A Cheers, Brent” March 19, 2019 Brent@GMATPrepNow posted a reply to The number 1000 lies between two consecutive perfect squares in the Problem Solving forum “Let''s examine some perfect squares that are close to 1000 30² = 900 31² = 961 32² = 1024 So, 1000 lies between 961 (aka 31²) and 1024 (aka 32²) 1000 is closer to 1024 (aka 32²) than to 961 Answer: D Cheers, Brent” March 19, 2019 Brent@GMATPrepNow posted a reply to Danny spends$360 buying his favorite dolls. If he buy only in the Problem Solving forum
“Let L = cost of 1 LARGE LemonHead doll So L-1 = cost of 1 SMALL LemonHead doll If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. Let''s first write a "word equation": ...” March 18, 2019 Brent@GMATPrepNow posted a reply to Bea owns how many more CDs than Al owns? (1) If Bea gives 9 in the Data Sufficiency forum “Let A = number of CDs Al owns Let B = number of CDs Bea owns Target question: What is the value of B - A? Statement 1: If Bea gives 9 of her CDs to Al, then Al will own twice as many CDs as Bea owns. We can create the equation: 2(B - 9) = A+9 Expand left side to get 2B - 18 = A+9 ...” March 16, 2019 Brent@GMATPrepNow posted a reply to How many different 3-digit numbers are greater than 299 and in the Problem Solving forum “Take the task of creating the 3-digit numbers and break it into stages. Stage 1: Select the first digit (hundreds digit) Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways Stage 2: Select the second digit (tens digit) Since the second digit can be 0, 2, 3, 4, ...” March 15, 2019 Brent@GMATPrepNow posted a reply to The cost of delivery for an order of desk chairs was$10.00 in the Data Sufficiency forum
“Target question: Is n > 24? Given: The cost of delivery for an order of desk chairs was $10.00 for the 1st chair, and$1 for each additional chair in the order. The office manager placed an order for n desk chairs. Statement 1: The delivery cost for the order totaled more than $30.00 ...” March 15, 2019 Brent@GMATPrepNow posted a reply to What is the average (arithmetic mean) of eleven consecutive in the Data Sufficiency forum “There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median." Since the consecutive integers are equally-spaced, their mean and median will be equal. Target question: What is the average of eleven consecutive integers? ...” March 15, 2019 e-GMAT posted a new topic called GMAT Quantitative: Question of the Week in the GMAT Math forum “Dear all, We have started a new series of questions and discussions, in the form of “Question of the Week”. These questions are new, well researched and bundled with important takeaways, which will definitely help you in reaching a 700+ score in GMAT. • Every week we will post a new ...” March 15, 2019 e-GMAT posted a new topic called e-GMAT Question of the Week #1 in the Problem Solving forum “The number n is the product of the first 49 natural numbers. What is the maximum possible value of p + q such that both $$\frac{n}{24^p}$$ and $$\frac{n}{36^q}$$ are integers? A. 11 B. 15 C. 20 D. 26 E. 30 To access all questions: Consolidated list of Questions of the Week” March 15, 2019 Brent@GMATPrepNow posted a reply to If 320 people attended the wedding and 200 attendees drank in the Data Sufficiency forum “This question is somewhat ambiguous, since it''s hard to say whether "nondrinkers" in statement 1 refers to people who drank neither beer nor wine, or did not drink beer. I''m assuming that it means to not drink beer, so I''ve add that to the question below. One approach is to use ...” March 14, 2019 Brent@GMATPrepNow posted a reply to Set X consists of different positive numbers arranged in in the Data Sufficiency forum “Target question: What is the arithmetic mean of set X? Given: Set X consists of different positive numbers arranged in ascending order: K, L, M, 5, 7. K, L and M are consecutive integers This means that EITHER K, L, M = 1, 2, 3 respectively, OR K, L, M = 2, 3, 4 respectively Head straight ...” March 14, 2019 Brent@GMATPrepNow posted a reply to combinations in the Problem Solving forum “Sure thing. Number of outcomes that OBEY the restriction = (total # of outcomes that IGNORE the restriction) - (# of outcomes that BREAK the restriction) total # of outcomes that IGNORE the restriction Select any 3 people from the 8 people We can do this in 8C3 ways (= 56 ways) # of ...” March 13, 2019 Brent@GMATPrepNow posted a reply to If when x is divided by z, the result is y remainder q, then in the Problem Solving forum “When it comes to remainders, there''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we ...” March 13, 2019 Brent@GMATPrepNow posted a reply to If$5,000 invested for one year at p percent simple annual i in the Data Sufficiency forum
“The great thing about DS questions is that we aren''t required to perform calculations if we know that we COULD perform those calculations. Here''s what I mean: Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ? ...”
March 13, 2019
Brent@GMATPrepNow posted a reply to If xyz ≠ 0, is x^3y^4z^5 > 0? in the Data Sufficiency forum
“ Given: xyz ≠ 0 Target question: Is x³y⁴z⁵ > 0? This is a great candidate for rephrasing the target question. Since we know that x² must be POSITIVE, we can safely take the inequality x³y⁴z⁵ > 0 and divide both sides by x² to get: xy⁴z⁵ > 0 Similarly, since ...”
March 13, 2019
Brent@GMATPrepNow posted a reply to Set M is composed of the positive even integers up to 100. in the Problem Solving forum
“Set M is composed of the positive even integers up to 100. Set M = {2, 4, 6, 8, . . . . 96, 98, 100} Set N is composed of the odd integers from –1 to 99 Set N = {-1, 1, 3, 5, . . . 95, 97, 99} What is the value of (the sum of Set M) – (the sum of Set N)? SUM of set M = 2 + 4 + 6 + 8 + ...”
March 13, 2019
Brent@GMATPrepNow posted a reply to A certain ball was dropped from a window 8 meters above a in the Problem Solving forum
“Drop 8 meters Rise 4 meters Drop 4 meters Rise 2 meters Drop 2 meters Rise 1 meters (DONE!) 8 + 4 + 4 + 2 + 2 + 1 = 21 meters Answer: A Cheers, Brent”
March 13, 2019
Brent@GMATPrepNow posted a reply to A certain hotel has 1,400 single rooms and 420 double rooms. in the Problem Solving forum
“The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes So, one person can clean 4 single rooms in ONE HOUR In other words, it takes 1 WORKER HOUR to clean 4 single rooms 1400/4 = 350 So, it takes 350 WORKER HOURS to clean 1400 rooms The hotel has 420 ...”
March 13, 2019
Brent@GMATPrepNow posted a reply to The number of candidates rejected in a certain admission pro in the Problem Solving forum
“The number of candidates rejected in a certain admission process was four times GREATER than the number of candidates accepted. Let x = the number of candidates accepted So, x + 4x = the number of candidates rejected In other words, 5x = the number of candidates rejected So, 6x = TOTAL number ...”
March 13, 2019
Brent@GMATPrepNow posted a reply to In a group of 24 musicians, some are pianists and the rest a in the Problem Solving forum
“In a group of 24 musicians, some are pianists and the rest are violinists. Let x = number of pianists So, 24-x = number of violinists Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. So, the number of pianists in the union = x/2 And the number of violinists in ...”
March 12, 2019
Brent@GMATPrepNow posted a reply to Carmen currently works 30 hours per week at her part-time jo in the Data Sufficiency forum
“ Given: Carmen currently works 30 hours per week Target question: If Carmen''s gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? This is a good candidate for rephrasing the target ...” March 11, 2019 Brent@GMATPrepNow posted a reply to W, X, Y and Z are four different positive integers. When X in the Problem Solving forum “ Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 ...” March 11, 2019 Brent@GMATPrepNow posted a reply to What is the hundredths digit of the decimal z? in the Data Sufficiency forum “Target question: What is the hundredths digit of the decimal z? Statement 1: The tenths digit of 100z is 2 Notice what happens when we take a decimal like 0.123456 and multiply it by 100. We get 12.345 (the tenths digit is 3) In the original decimal, the 3 was in the thousandths place. ...” March 10, 2019 Brent@GMATPrepNow posted a new topic called W, X, Y and Z are four different positive integers. When X in the Problem Solving forum “W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W? A) 19 B) 20 C) 21 D) 22 E) 23 Source: www.gmatprepnow.com Difficulty level: 650 - 700” March 10, 2019 Brent@GMATPrepNow posted a reply to If 4x − 3y = 13 and 5x + 2y = − 1, then x = in the Problem Solving forum “GIVEN: 4x − 3y = 13 5x + 2y = − 1 Take the TOP equation and multiply both sides by 2 Take the BOTTOM equation and multiply both sides by 3 We get: 8x - 6y = 26 15x + 6y = -3 ADD the two equations to get: 23x = 23 Solve: x = 23/23 = 1 Answer: C Cheers, Brent” March 10, 2019 Brent@GMATPrepNow posted a reply to W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “Target question: What is the value of Z? Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with ...” March 8, 2019 Brent@GMATPrepNow posted a reply to OG 2017 Ratio Question in the Data Sufficiency forum “Target question: What is the total number of articles of clothing in the closet? Given: The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If shirts : dresses : jackets = 9 : 4 : 5, then there are infinitely many ...” March 7, 2019 Brent@GMATPrepNow posted a new topic called W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. What is the value of Z? 1) W = X – 4 2) W + Z = 4 Difficulty level: 650 – 700 Source: www.gmatprepnow.com” March 7, 2019 Brent@GMATPrepNow posted a reply to 60 DAY STUDY GUIDE ENQUIRY in the Ask a GMAT Prep Now representative forum “Sorry, but there are no plans to update the 60-day guide in the near future. Cheers, Brent” March 7, 2019 Brent@GMATPrepNow posted a reply to What is the sum of all of the integers in the chart above? in the Problem Solving forum “Always check the answer choices BEFORE solving the question!! Since the answer choices are nicely spread apart, we can be quite aggressive in our estimation Let''s add the 5 numbers in each COLUMN COLUMN 1: Sum ≈500 COLUMN 2: Sum ≈-1000 COLUMN 3: Sum ≈1500 COLUMN 4: Sum ≈-2000 ...” March 6, 2019 Brent@GMATPrepNow posted a reply to If 0.02 < x < 0.04 and 100 < y < 250, which of t in the Problem Solving forum “We can use a nice (and often tested) fraction property that says: (a - b)/c = a/c - bc So, (y-x)/(xy) = y/xy - x/xy = 1/x - 1/y That''s better! So, we''re now looking for a possible value of 1/x - 1/y Let''s look at some EXTREME values. We can MAXIMIZE the value of 1/x - 1/y by MAXIMIZING ...” March 6, 2019 Brent@GMATPrepNow posted a reply to For every even positive integer m, f(m) represents the in the Problem Solving forum “f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24 Rewrite as prime factorization: f(24) = 2 x (2)(2) x (2)(3) x (2)(2)(2) x (2)(5) x (2)(2)(3) x (2)(7) x (2)(2)(2)(2) x (2)(3)(3) x (2)(2)(5) x (2)(11) x (2)(2)(2)(3) Answer: E ASIDE: As you can see from the answer choice, I ...” March 6, 2019 Brent@GMATPrepNow posted a reply to Is xy>3? in the Data Sufficiency forum “Target question: Is xy > 3 ? Statement 1: (7^x) > 729 Since there''s no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7 Since there''s no information about x, we cannot answer the target question with ...” March 5, 2019 Brent@GMATPrepNow posted a reply to x is the product of all even numbers from 2 to 50, inclusive in the Problem Solving forum “Here''s a very similar (official) question to practice with: https://www.beatthegmat.com/arthemetic-question-on-factors-and-prime-numbers-t275643.html Cheers, Brent” March 5, 2019 Brent@GMATPrepNow posted a reply to Joey works at a clothing store and receives an employee in the Problem Solving forum “Let R = REGULAR price of the item Joey and receives an employee discount of 10 percent off the regular price of any item. So, Joey pays 90% of the REGULAR price. In other words, 0.9R = the DISCOUNT price that Joey actually pays What is the regular price of an item that Joey purchases for ...” March 5, 2019 Brent@GMATPrepNow posted a reply to In how many ways can 16 different gits be divided among four in the Problem Solving forum “Let''s say the children are named A, B, C, and D Stage 1: Select 4 gifts to give to child A Since the order in which we select the 4 gifts does not matter, we can use combinations. We can select 4 gifts from 16 gifts in 16C4 ways (= 16!/(4!)(12!)) So, we can complete stage 1 in ...” March 4, 2019 Brent@GMATPrepNow posted a reply to The positive two-digit integers x and y have the same digits in the Problem Solving forum “Another approach is to test some values for x and y that satisfy the given information. Positive two-digit integers x and y have the same digits, but in reverse order So, it COULD be the case that x = 12 and y = 21 Which of the following must be a factor of x + y? x + y = 12 + 21 = 33 ...” March 3, 2019 Brent@GMATPrepNow posted a reply to Median of set T in the Problem Solving forum “If we have a set of y INTEGERS, there are two possible cases when it comes to the MEDIAN. Case a: y is an ODD number, in which case the MEDIAN equals the one middle integer (when all of the integers are arranged in ascending order). In this case, the median must be an integer. Case b: y is an ...” March 2, 2019 Brent@GMATPrepNow posted a reply to Two positive numbers differ by 12 and their reciprocals in the Problem Solving forum “Two positive numbers differ by 12 Let x = the smaller number So x + 12 = the larger number NOTE: our goal is to find the value of x(x + 12) Their reciprocals differ by 4/5 We get: 1/x - 1/(x+12) = 4/5 Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5 Multiply both sides by 5 to get: 5 ...” February 28, 2019 Brent@GMATPrepNow posted a reply to In a town of 8,000 residents, 65 percent of all residents in the Problem Solving forum “Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of residents, and the two characteristics are: ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum “Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...” February 28, 2019 Brent@GMATPrepNow posted a reply to A certain club has 20 members. What is the ratio of the in the Problem Solving forum “5-member committees Since the order in which we select the committee members does not matter, we can use COMBINATIONS We can select 5 people from 20 people in 20C5 ways 20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) 4-member committees Since the order in which we select the committee members ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Train A and Train B began traveling towards each other from in the Problem Solving forum “This is a SHRINKING GAP question. Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, 35 mph + 25 mph = 60 mph So, the gap CLOSES at a rate of 60 mph Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM ...” February 28, 2019 Brent@GMATPrepNow posted a reply to In 1990 the budgets for projects Q and V were$660,000 and in the Problem Solving forum
“One approach is to treat this is a rate question. In 1990 the GAP BETWEEN V''s budget and Q''s budget was $120,000 ($780,000 - $660,000 =$120,000) Each year, the budget for Q increased by $30,000 and the budget for V decreased by$10,000. In other words, the GAP BETWEEN the budgets ...”
February 28, 2019
Brent@GMATPrepNow posted a reply to Is xy+zt+yz+tx positive? in the Data Sufficiency forum
“Target question: Is xy + zt + yz + tx positive? Statement 1: |x| = |y| = |z| = t Let''s TEST some values. There are several values of x, y, z and t that satisfy statement 1. Here are two: Case a: x = y = z = t = 1. In this case, xy + zt + yz + tx = (1)(1) + (1)(1) + (1)(1) + (1)(1) = 4. ...”
February 26, 2019
Brent@GMATPrepNow posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum
“This is a tough one to use the INPUT-OUTPUT approach, but here is goes: Let c = $2 (it cost$2 to make each umbrella) Let x = 10 (we make 10 umbrellas) Let r = $5 (the retail price is$5 per umbrella) Let b = $0 (the below-cost sale price is$0 per umbrella) So, the manufacturer made 10 ...”
February 26, 2019
Brent@GMATPrepNow posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum
“After about 30 seconds, I recognized that I couldn''t see a nice straightforward solution (one that doesn''t involve considering multiple cases), so I had 3 options: 1) Keep searching for a nice straightforward solution 2) Guess and move on 3) List the possible outcomes Since the answer ...”
February 25, 2019
Brent@GMATPrepNow posted a reply to Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum
“ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8 Take the task of removing the 9 chips and break it into stages. Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways Stage 2: Select an EVEN number to be the 2nd selection ...”
February 25, 2019
Brent@GMATPrepNow posted a reply to All assets in Karina's investment portfolio are divided betw in the Problem Solving forum
“Let''s say Karina''s entire portfolio is worth $100 altogether. So, we want to divide this$100 into four integer amounts: w, x, y, z, where w < x < y < z, and we want to minimize the value of z In order to MINIMIZE the value of the z, we must MAXIMIZE the values of w, x, and y. Now ...”
February 25, 2019
Brent@GMATPrepNow posted a reply to Vivian drives to her sister’s house and back. She takes th in the Problem Solving forum
“One approach is to assign a "nice" value (one that works well with 50 mph and 70 mph) to the distance her sister''s house. So, let''s say the distance is 350 miles Average speed = (total distance traveled)/(total travel time) TOTAL distance = 350 miles + 350 miles = 700 miles ...”
February 25, 2019
Brent@GMATPrepNow posted a reply to In a certain class, the ratio of girls to boys is 5:4. How m in the Data Sufficiency forum
“ Given: In a certain class, the ratio of girls to boys is 5:4. Let G = number of girls in the class Let B = number of boys in the class We can write: G/B = 5/4 Cross multiply to get: 4G = 5B Rearrange to get: 4G - 5B = 0 Target question: What is the value of G Statement 1: If four ...”
February 24, 2019
Brent@GMATPrepNow posted a reply to Kim has 40 percent more money than Sal and Sal has 20 in the Problem Solving forum
“Let x = Phil''s money Sal has 20 percent LESS money than Phil So, Sal''s money = (Phil''s money) - (20% Phil''s money) = x - (20% of x) = x - 0.2x = 0.8x Kim has 40 percent more money than Sal So, Kim''s money = (Sal''s money) + (40% Sal''s money) = (0.8x) + (40% of 0.8x) = ...”
February 24, 2019
Brent@GMATPrepNow posted a reply to A straight line in the xy-plane has a slope of 2 and a in the Problem Solving forum
“The question conveniently gives us the information to write the equation of the line in slope y-intercept form, y = mx + b, where m = slope and b = the y-intercept. Line in the xy-plane has a slope of 2 and a y-intercept of 2 So, the equation of the line is: y = 2x + 2 On this line, what is ...”
February 24, 2019
Brent@GMATPrepNow posted a reply to If y >= 0, What is the value of x? in the Data Sufficiency forum
“Target question: What is the value of x? Given: y ≥ 0 Statement 1: |x - 3| ≥ y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 10 and y = 2. We get |10 - 3| ≥ 2, which evaluates to be 7 ≥ 2, which satisfies ...”
February 23, 2019
Brent@GMATPrepNow posted a reply to The total of company C's assets in 1994 was 300% greater in the Problem Solving forum
“The total of company C''s assets in 1992 was N dollars Company C''s assets in 1993 was 400% greater than the total in 1992 So, 1993 assets = (1992 assets) + (400% of 1992 assets) = (N) + (400% of N) = (N) + (400/100 x N) = N + 4N = 5N Company C''s assets in 1994 was 300% greater than the ...”
February 23, 2019
Brent@GMATPrepNow posted a reply to At a bakery, the price of a bagel ranges between $0.65 and$ in the Problem Solving forum
“The least expensive price for a bagel is $0.65 If a customer purchases 12 bagels (at$0.65 each), then he/she receives 13 bagels. So, the minimum amount that a customer could pay to receive 13 bagels = 12 x $0.65 =$7.80 Answer: B Cheers, Brent”
February 23, 2019
Brent@GMATPrepNow posted a reply to a, b, and c are positive integers. Is a+b+c an odd number? in the Data Sufficiency forum
“ Given: a, b, and c are positive integers. Target question: Is a + b + c an odd number? Statement 1: ab is an odd number No information about c. NOT SUFFICIENT Statement 2: c is an odd number No information about a or b. NOT SUFFICIENT Statements 1 and 2 combined If ab ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to In how many ways a cricket team consisting of 5 batsmen, 4 in the Problem Solving forum
“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to If 1/x-1/y=1/z, what is the value of y, in terms of x and z? in the Problem Solving forum
“We can also solve the question algebraically. GIVEN: 1/x - 1/y = 1/z Multiply both sides by x to get: 1 - x/y = x/z Multiply both sides by y to get: y - x = xy/z Multiply both sides by z to get: yz - xz = yx Rearrange to get y terms on one side: yz - yx = xz Factor left side: y(z - x) = ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 in the Problem Solving forum
“A quick solution is to assign some values to the highest paid and lowest paid workers Let $10,000 = the lowest salary LAST YEAR Let$40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = $30,000 If the annual salary of each of the 100 employees this ...” February 21, 2019 Brent@GMATPrepNow posted a reply to The sum of two integers is 27. The larger integer is 25% in the Problem Solving forum “Let x = the smaller integer So, 1.25x = the larger integer (since the larger integer is 25% greater than the smaller integer) The sum of two integers is 27. We can write: x + 1.25x = 27 Simplify: 2.25x = 27 Solve: x = 27/2.25 IMPORTANT: What''s a nice fast way to evaluate 27/2.25? An easy ...” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the greatest positive three-digit number that is div in the Problem Solving forum “One approach is to check each answer choice, beginning with the largest answer choice E. 840 840 is divisible by 2, 3, 4, 5, 6 and 7 Answer: E Cheers, Brent” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the largest digit n for which the number 123,45n is in the Problem Solving forum “RULE: if the SUM of the digits of a number is divisible by 3, then that number is divisible by 3 Take, for example, the number 1,001,226 1 + 0 + 0 + 1 + 2 + 2 + 6 = 12 Since 12 is divisible by 3, we know that 1,001,226 is divisible by 3 If 123,45n is divisible by 3, then 1 + 2 + 3 + 4 + 5 + n ...” February 21, 2019 Brent@GMATPrepNow posted a reply to In the figure above, the angle marked at c has been created in the Data Sufficiency forum “Target question: What is the sum of a, b, and c? This is a good candidate for rephrasing the target question. Since angles on a line add to 180°, we already know that b + c = 180 We get: a + b + c = a + 180 So, in order to find the sum of a, b and c, we need only find the value of a ...” February 21, 2019 Brent@GMATPrepNow posted a reply to At a certain committee meeting only associate professors and in the Problem Solving forum “Notice that the question asks us to find that TOTAL number of people present. In other words, it the question does NOT ask us to find the number of associate professors or assistant professors present. Since each person brings THREE items, and since total of 21 items were brought (10 pencils ...” February 21, 2019 Brent@GMATPrepNow posted a reply to In a class of 30 students, 2 students did not borrow any in the Problem Solving forum “The average (arithmetic mean) number of book borrowed per student was 2. Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60 2 students borrowed 0 books: total of 0 books 12 students borrowed 1 book each: total of 12 books 10 students borrowed 2 books ...” February 21, 2019 Brent@GMATPrepNow posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “Target question: Is each of the numbers n the list equal to zero? Given: There are more than 2 numbers in the list Statement 1: The product of any 2 numbers in the list is ZERO There are several possible sets that satisfy this condition. Here are two: Case a: the set is {0, 0, 0} in ...” February 21, 2019 Brent@GMATPrepNow posted a reply to Is mn < 10? in the Data Sufficiency forum “Target question: Is mn < 10? Statement 1: m < 5 and n < 2 Let''s TEST some values. There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 0 and n = 0. In this case mn = (0)(0) = 0. So, the answer to the target question is YES, mn IS less than 10 ...” February 20, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency lesson #4: GMAT Data Sufficiency Strategies - Part I Video : https://www.youtube.com/watch?v=Ep09hi1OJpI Cheers, Brent” February 20, 2019 Brent@GMATPrepNow posted a reply to John takes 15 hours to complete a certain job, while Bill ta in the Problem Solving forum “Let''s first see what happens if Steven works as fast as possible. Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours. For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job. Unfortunately, ...” February 20, 2019 Brent@GMATPrepNow posted a reply to If x, y, and z are three-digit positive integers and if x = in the Data Sufficiency forum “Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. ...” February 20, 2019 Brent@GMATPrepNow posted a reply to George bought a large electronic item with a 15% off coupon in the Problem Solving forum “George was SUPPOSED to receive a 15% discount, but he received a 30% discount. So, he should have returned 15% of the original cost. However, the manager asked for half that amount (i.e., 7.5% of the original cost) In other words, 7.5% of the original cost =$40.50 IMPORTANT: at this point, ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Is x-y+1 greater than x+y-1 ? in the Data Sufficiency forum
“Target question: Is x - y + 1 > x + y - 1 ? This is a good candidate for rephrasing the target question. Take: x - y + 1 > x + y - 1 Subtract x from both sides to get: -y + 1 > y - 1 Add y to both sides to get: 1 > 2y - 1 Add 1 to both sides to get: 2 > 2y Divide both ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Anna has to visit at least 2 European cities on her vacation in the Problem Solving forum
“We need to consider 3 different cases: i) Anna visits 2 cities ii) Anna visits 3 cities iii) Anna visits 4 cities i) Anna visits 2 cities There are 4 options for the FIRST city and 3 options for the SECOND city So, the total number of 2-city itineraries = (4)(3) = 12 ii) Anna visits 3 ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Which of the following points is the intersection between in the Problem Solving forum
“KEY CONCEPT: The point of intersection (call P) of the lines y = 3x + 6 and y = -2x - 4 will be such that the x- and y-coordinates of P will satisfy BOTH equations. Since both equations are set equal to y, we can write: 3x + 6 = -2x - 4 Add 2x to both sides: 5x + 6 = - 4 Subtract 6 from both ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to How many positive perfect cubes are divisors of 4^6? in the Problem Solving forum
“4⁶ = (2²)⁶ = 2¹² Since 2¹² = (2³)(2⁹), we know 2³ is a divisor of 2¹² Since 2¹² = (2⁶)(2⁶), we know 2⁶ is a divisor of 2¹² Since 2¹² = (2⁹)(2³), we know 2⁹ is a divisor of 2¹² Since 2¹² = (2¹²)(2⁰), we know 2¹² is a divisor of 2¹² Since 2¹² = ...”
February 18, 2019
Brent@GMATPrepNow posted a reply to The squares of two consecutive positive integers differ by 5 in the Problem Solving forum
“Let x = the smaller integer So, x+1 = the larger integer (since the numbers are CONSECUTIVE) The squares of two consecutive positive integers differ by 55. We can write: (x + 1)² - x² = 55 Expand: x² + 2x + 1 - x² = 55 Simplify: 2x + 1 = 55 So: 2x = 54 Solve: x = 54/2 = 27 Answer: ...”
February 18, 2019
Brent@GMATPrepNow posted a reply to A scientist has 400 units of a 6% phosphoric acid solution, in the Problem Solving forum
“We can solve this question with the weighted averages formula: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let x = the number of units of 12% phosphoric acid solution needed ...”
February 16, 2019
Brent@GMATPrepNow posted a reply to If a = 15! + 13, which of the following are factors of a? I in the Problem Solving forum
“Here''s a similar question to practice with: https://www.beatthegmat.com/divisibility-t111432.html Cheers, Brent”
February 16, 2019
Brent@GMATPrepNow posted a reply to Phone plan A charges $1.25 for the first minute and$0.15 in the Problem Solving forum
“Phone plan A charges $1.25 for the first minute and$0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call = $1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay$1.25 for the FIRST minute. So, if x = ...”
February 16, 2019
Brent@GMATPrepNow posted a reply to A magician has five animals in his magic hat: 3 doves and 2 in the Problem Solving forum
“Let''s apply probability rules First notice that, to get a matched pair, we can select 2 doves or 2 rabbits. So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove) We can now apply our AND and OR rules to get: P(matched pair) = x P(2nd ...”
February 16, 2019
Brent@GMATPrepNow posted a reply to If a positive integer q is divisible by both 3 and 11, then in the Problem Solving forum
“I. 14 14 is NOT divisible by 3 or 11 So, statement I is NOT true. ELIMINATE A and D III. 66 Integer q COULD equal 33 (which is divisible by 3 and 11) Since 33 is NOT divisible by 66, statement III is NOT true. ELIMINATE C and E By the process of elimination, the correct answer is B ...”
February 15, 2019
Brent@GMATPrepNow posted a reply to Kevin buys beer in bottles and cans. He pays $1.00 for each in the Data Sufficiency forum “Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can ...” February 15, 2019 Brent@GMATPrepNow posted a reply to A group of x people is practicing levitation yoga. One-fourt in the Problem Solving forum “ One-fourth of the people rise up in the air If 1/4 of the x people are in the AIR, the remaining 3/4 of the x people are on the GROUND So, (3/4)x = number of people on the GROUND After a while, 3 of them come back down. So, the number of people on the GROUND is increased by 3 So, now ...” February 14, 2019 Brent@GMATPrepNow posted a reply to In the figure above, polygon N has been partially covered by in the Data Sufficiency forum “Target question: How many sides does N have? Statement 1: x + y = 45 Since all angles in a triangle add to 180°, we know that the missing angle is 135° https://i.imgur.com/oUCDRTN.png There are plenty of polygons that have at least one angle measuring 135°. Here are two: Case a: ...” February 14, 2019 Brent@GMATPrepNow posted a reply to Which of the following expressions is equal to 2^32-2^31-2^3 in the Problem Solving forum “2^32 - 2^31 - 2^30 = (2^30)(2^2 - 2^1 - 1) = (2^30)(4 - 2 - 1) = (2^30)(1) = 2^30 Answer: C Cheers, Brent” February 14, 2019 Brent@GMATPrepNow posted a reply to OG L-shaped garden in the Data Sufficiency forum “Target question: What is the value of k? Statement 1: The area of the garden is 189 square feet. Let''s drawn an auxiliary line that divides the shape into two rectangular regions A and B. https://i.imgur.com/hJBOxsO.png Regions A and B have the following measurements. ...” February 13, 2019 Brent@GMATPrepNow posted a reply to How many integers between 18 and 3399 are multiples of 17? in the Problem Solving forum “Let''s list the multiples of 17 that are between 18 and 3399 : 34 = 2(17) 51 = 3(17) 68 = 4(17) 85 = 5(17) . . . 3383 = 199(17) So, the number of multiples of 17 is EQUAL to the number of integers from 2 to 199 inclusive ASIDE: A nice rule says: the number of integers from x to y ...” February 13, 2019 Brent@GMATPrepNow posted a reply to A mountain resort will hold its annual one-day snowboarding in the Problem Solving forum “GIVEN: P(snow) = 0.7, so P(no snow) = 0.3 Let''s use the complement to solve this. That is, P(event is held) = 1 - P(event is NOT held) P(event is NOT held) = P(no snow on Saturday AND no snow on Sunday) = P(no snow on Saturday) x P(no snow on Sunday) = 0.3 x 0.3 = 0.09 So, P(event is ...” February 13, 2019 Brent@GMATPrepNow posted a reply to The product P of two prime numbers is between 9 and 55. in the Problem Solving forum “Prime numbers that are greater than 2 but less than 6: 3, 5 Prime numbers that are greater than 13 but less than 25: 17, 19, 23 Scan the answer choices . . . E) 51 = 3 x 17 PERFECT! Answer: E Cheers, Brent” February 12, 2019 Brent@GMATPrepNow posted a reply to What is the probability that you get a pair when picking the in the Problem Solving forum “P(select pair) = P(1st card is ANY card AND 2nd card matches 1st card) = P(1st card is ANY card) x P(2nd card matches 1st card) = 1 x 3/51 = 3/51 = 1/17 = C Aside: P(2nd card matches 1st card) = 3/51, because once 1 card is selected, there are 51 cards remaining in the deck. Among those 51 ...” February 12, 2019 Brent@GMATPrepNow posted a reply to At her current job, Mary gets a 1.5% raise twice per year. in the Problem Solving forum “One approach here is to apply the COMPOUND INTEREST formula. However, if you didn''t see that the question is analogous to a COMPOUND INTEREST question, we can also solve the question by looking for a pattern. Let''s try that: Time elapsed (in years) | salary 0 | s 0.5 | (1.015)(s) 1 | ...” February 12, 2019 Brent@GMATPrepNow posted a reply to Of the 3,000 cars manufactured in Factory Q last year, how in the Data Sufficiency forum “Target question: Of the 3,000 cars manufactured in Factory Q LAST YEAR, how many were still in operation at the end of the year? Neither statement provides any information about the cars manufactured LAST YEAR. Instead, we''re told about ALL of the cars ever manufactured . As such, the ...” February 12, 2019 Brent@GMATPrepNow posted a reply to In the figure given, x = 3(y-z). What is the value of x? in the Problem Solving forum “Since angles on a LINE add to 180°, . . . https://i.imgur.com/kAdhC7N.png . . . we know that x + z = 180 Subtract x from both sides to get: z = 180 - x Since angles in a CIRCLE add to 360°. . . https://i.imgur.com/l1SKqw5.png . . . we know that 60 + (180 - x) + y = 360 Simplify left ...” February 12, 2019 Brent@GMATPrepNow posted a reply to In the xy-coordinate plane, if the point (0,2) lies on the g in the Problem Solving forum “KEY CONCEPT: In order for a point to be ON a line, the x- and y-coordinates of the point must satisfy the equation of that line So, for example, the point (3,7) lies ON the line defined by the equation y = 2x + 1, because x = 3 and y = 7 satisfy the equation y = 2x + 1 That is, 7 = 2(3) + 1 ...” February 12, 2019 Brent@GMATPrepNow posted a reply to Set S consists of n consecutive integers, where n > 1. in the Data Sufficiency forum “ Given: Set S consists of n consecutive integers, where n > 1. Target question: What is the value of n? IMPORTANT: Notice that the two statements are VERY SIMILAR. That is, if the sum of the values is 14 (statement 2), then it is guaranteed that the sum is divisible by 7 (statement 1). ...” February 12, 2019 Brent@GMATPrepNow posted a reply to A computer chip manufacturer expects the ratio of the number in the Problem Solving forum “Let''s find some TOTALS for all 4 shipments combined. There are 51,000 chips altogether There are 17 defective chips altogether. So, 17/51000 of the chips are defective. (notice that 17 divides nicely into 51000!) SIMPLIFY: 1/3000 of the chips are defective So, if we have a shipment of ...” February 11, 2019 Brent@GMATPrepNow posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum “Since angles in a triangle add to 180°, we know that the missing angle = (90 - 2x)° https://i.imgur.com/FcSiZi2.png Aside: Notice that (90 - 2x)° + 90° + 2x° =180° Since angles on a line add to 180°, we know that the missing angle = (90 + 2x)° https://i.imgur.com/9Z5ULFo.png ...” February 11, 2019 Brent@GMATPrepNow posted a reply to tough geo. problem in the Data Sufficiency forum “Target question: What is the length of side BC? Statement 1: Line segment AD has length 6. BEFORE we deal with statement 1, let''s see what information we can add to the diagram. For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC: ...” February 11, 2019 Brent@GMATPrepNow posted a reply to What is the area of a right triangle? in the Data Sufficiency forum “Target question: What is the area of a right triangle? Statement 1: The length of one side is 3 Knowing the length of only 1 side will not help us answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: The length of one side is 4 NOT SUFFICIENT (same ...” February 11, 2019 Brent@GMATPrepNow posted a reply to If x=0.2, then what is the value of x^3-1/x-1? in the Problem Solving forum “Some spaces and/or brackets would definitely help here. Do you mean x^3 - 1/x - 1 or x^3 - 1/(x - 1) or (x^3 - 1)/(x - 1)?? Cheers, Brent” February 11, 2019 Brent@GMATPrepNow posted a reply to If n and p are integers, is p > 0? in the Data Sufficiency forum “ Given: n and p are integers Target question: Is p > 0? Statement 1: n + 1 > 0 No information about p. Statement 1 is NOT SUFFICIENT Statement 2: np > 0 There are several values of n and p that satisfy statement 2. Here are two: Case a: n = 1 and p = 1. In this case, ...” February 11, 2019 Brent@GMATPrepNow posted a reply to If x and y are integers, is x^2-y^2 odd? in the Data Sufficiency forum “Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is x² - y² odd? IMPORTANT: Notice that we can factor x² - y² to get: x² - y² = (x + y)(x - y) ...” February 10, 2019 Brent@GMATPrepNow posted a reply to In a group of 100 adults, 75 percent of the women are in the Problem Solving forum “GIVEN: 75% women are LEFT handed This also tells us that 25% women are RIGHT handed GIVEN: There are 12 right-handed women Let W = total number of women in the group So, 25% of W = 12 Rewrite as: 0.25W = 12 Solve: W = 12/0.25 = 48 So, there are 48 women So, the number of men in the ...” February 10, 2019 Brent@GMATPrepNow posted a reply to Triangle XYZ is an isosceles right triangle. If side XY is l in the Problem Solving forum “Triangle XYZ is an isosceles right triangle. Let''s sketch an isosceles right triangle: https://i.imgur.com/N3UOppf.png Side XY is longer than side YZ Since the hypotenuse is the longest side of a right triangle, side XY must be the hypotenuse. Add this to our diagram: ...” February 9, 2019 Brent@GMATPrepNow posted a reply to Out of 2 broken TV sets and 6 fixed TV sets in Joe's Fix-My- in the Problem Solving forum “There are 8 TV''s in total 2 are broken 6 are fixed We want to find P(at least one TV is broken) When it comes to probability questions involving at least, it''s often best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting ...” February 8, 2019 Brent@GMATPrepNow posted a reply to An electrical supplies store sells 140 power stabilizer in the Problem Solving forum “Let x = the selling price per unit So, x - 16 = the PROFIT on ONE unit And 140(x - 16) = the PROFIT on the sale of 140 units (aka the weekly profit) What is the minimum selling price per unit that will ensure a weekly profit of at least$5600 from sales of power stabilizers? In other words, ...”
February 8, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Target question: What is the remainder when the positive integer n is divided by 6? Statement 1: n is multiple of 5 Let''s TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 10. In this case, the answer to the target question is the ...”
February 8, 2019
Brent@GMATPrepNow posted a reply to What is the sum of the digits of the number (2^{2018})(5^{20 in the Problem Solving forum
“Useful rule: (x^k)(y^k) = (xy)^k Example: (3^4)(7^4) = 21^4 (2^2018)(5^2019)(3^2) = (2^2018)((5^2018)(5^1))(3^2) = (2^2018)(5^2018)(5^1))(3^2) = (10^2018)(5^1))(3^2) = (10^2018)(5)(9) = (10^2018)(45) We know that (10^2018) = 1 followed by 2018 zeros So, (10^2018)(45) = 45 followed by ...”
February 7, 2019
Brent@GMATPrepNow posted a reply to If a and b are integers, is a + b + 3 an odd integer? (1) in the Data Sufficiency forum
“Target question: Is a + b + 3 an odd integer? Given: a and b are integers Statement 1: ab is an odd integer. Some useful rules: 1. ODD - ODD = EVEN 2. ODD - EVEN = ODD 3. EVEN - ODD = ODD 4. EVEN - EVEN = EVEN 5. (ODD)(ODD) = ODD 6. (ODD)(EVEN) = EVEN 7. (EVEN)(EVEN) = EVEN ...”
February 7, 2019
Brent@GMATPrepNow posted a reply to The sides of a right triangle are consecutive even integers, in the Problem Solving forum
“GIVEN: p = length of the longest side Since the side lengths are consecutive even integers, we can say: p - 2 = length of the 2nd longest side p - 4 = length of the shortest side NOTE: The longest side is the HYPOTENUSE. So, p = length of the HYPOTENUSE And p - 2 = length of one leg of ...”
February 7, 2019
Brent@GMATPrepNow posted a reply to In the diagram above, O is the center of the circle. What is in the Data Sufficiency forum
“Target question: What is the length of chord AC? Given: O is the center of the circle If O is the center of the circle, then AB is the circle''s DIAMETER If AB is the DIAMETER, then ∠C = 90°, because ∠C is an inscribed angle containing ("holding") the diameter. So, let''s ...”
February 7, 2019
Brent@GMATPrepNow posted a reply to Ten telegenic contestants with a variety of personality diso in the Problem Solving forum
“Let''s take the task of creating the teams and break it into stages. Stage 1: Select two 5 contestants to be in tribe A Since the order in which we select the contestants does not matter, we can use combinations. We can select 5 contestants from 10 contestants in 10C5 ways 10C5 = ...”
February 7, 2019
Brent@GMATPrepNow posted a reply to We define the harmonic mean of a set of numbers as the recip in the Problem Solving forum
“What is the harmonic mean of 20 and 30? NOTE: 20 = 20/1 So, the reciprocal of 20 = 1/20 And the reciprocal of 30 = 1/30 The average of 1/20 and 1/30 = (1/20 + 1/30 )/2 = (3/60 + 2/60 )/2 = (5/60 )/2 = (5/60 )/(2/1) = (5/60 )(1/2) = 5/120 The reciprocal of 5/120 = 120/5 = 24 Answer: ...”
February 6, 2019
Brent@GMATPrepNow posted a reply to A certain bag contains red, blue, and green marbles. What is in the Data Sufficiency forum
“ Given: A certain bag contains red, blue, and green marbles. Let R = # number red marbles in the bag Let B = # number blue marbles in the bag Let G = # number green marbles in the bag Target question: What is the value of G/R? Statement 1: The number of blue marbles in the bag is two ...”
February 6, 2019
Brent@GMATPrepNow posted a reply to If x is a nonzero number, which of the three numbers x, 1/x in the Data Sufficiency forum
“ Given: x is a nonzero number Target question: Which of the three numbers x, 1/x and x² is greatest? Statement 1: -1 < x < 1 This statement doesn''t FEEL sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = ...”
February 6, 2019
Brent@GMATPrepNow posted a reply to Three sisters have an average (arithmetic mean) age of 25 in the Problem Solving forum
“If the average age is 25, we can write: (sum of all 3 ages)/3 = 25 This means, the sum of all 3 ages = 75 If the median is 24, then we can express the ages in ascending order as follows: __ , 24, __ Since the sum of the ages is 75, we can MINIMIZE the age of the oldest girl by MAXIMIZING the ...”
February 5, 2019
Brent@GMATPrepNow posted a reply to A contractor combined x tons of a gravel mixture that in the Data Sufficiency forum
“Let''s use some weighted averages to solve this question Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Target question: What is the value of x ? Given: A contractor combined x ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to A committee of 6 is chosen from 8 men and 5 women so as to in the Problem Solving forum
“Since the committee must have 6 people, there are two cases that meet the given restrictions: 1) The committee has 2 men and 4 women 2) The committee has 3 men and 3 women 1) The committee has 2 men and 4 women Since the order in which we select the men and women does not matter, we can use ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to Mixture problem unclear in the Problem Solving forum
“When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED. Since we''re asked to find a PERCENTAGE, we can assign a "nice" value to the original volume. So, let''s say we start with 100 liters https://i.imgur.com/yt2KAw7.png As you can ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to Mr. Jones spends $25 on movie tickets for a party of adults in the Data Sufficiency forum “ Given: Mr. Jones spends$25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost $3 each and children''s tickets cost$2 each. There are several scenarios that satisfy statement 1. Here are ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to In a certain sock drawer, there are 4 pairs of black socks, in the Problem Solving forum
“If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don''t have a matching sock. So, we can select 3 socks WITHOUT having a matching pair. However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected. Answer: A Cheers, Brent”
February 4, 2019
Brent@GMATPrepNow posted a reply to Piper bought three shirts. The three shirts cost $210 in the Data Sufficiency forum “IMPORTANT: Notice that statements 1 and 2 provide the EXACT SAME INFORMATION. When this occurs, the correct answer is either D or E Since the information is so sparse, I have a feeling that the correct answer is E. So, I''m going to try to find two possible cases that satisfy both statements, yet ...” February 3, 2019 Brent@GMATPrepNow posted a reply to In the graduating class of a certain college, 48 percent of in the Problem Solving forum “I thought I''d point out that Mitch''s Double Matrix Method approach can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of students, and the two characteristics are: - male or female - younger than 25 ...” February 3, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency lesson #3: Avoiding Common Mistakes - Part I Video : https://www.youtube.com/watch?v=iACq36scVYQ Cheers, Brent” February 3, 2019 Brent@GMATPrepNow posted a reply to Beth has a collection of 8 boxes of clothing for a charity, in the Problem Solving forum “One box contains 12 items of clothing Let t, u, v, w, x, y, z = the number of items in each of the other 7 boxes Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. We can write: (t + u + v + w + x + y + z + ...” February 2, 2019 Brent@GMATPrepNow posted a reply to Perpendicular lines m and n... in the Data Sufficiency forum “ Given: Perpendicular lines m and n intersect at (0,b) Target question: What is the value of b? Statement 1: The slope of the line m is -1/2 Since line n is PERPENDICULAR to line m, we know that line n has slope 2 However, we can raise and lower the two lines so that the value of b is ...” February 1, 2019 Brent@GMATPrepNow posted a reply to How many females? (GMAT Prep 2) in the Data Sufficiency forum “Target question: What percent of the students in the class were females? Let''s use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a ...” January 30, 2019 Brent@GMATPrepNow posted a reply to A doctor prescribed 18 cubic centimeters of a certain drug t in the Problem Solving forum “We can use equivalent ratios to determine what the dosage SHOULD have been. We''ll use the ratio of drug dosage (in cubic centimeters)/body weight (in pounds) Let x = the dosage (in cubic centimeters) the patient SHOULD have received We get: 2/15 = x/120 Cross multiply to get: 15x = ...” January 30, 2019 Brent@GMATPrepNow posted a reply to Marla starts running around a circular track at the same... in the Problem Solving forum “Let t = the time (in HOURS) that it takes Marla to complete 4 more laps than Nick. So, after t hours, we can write: (Marla''s lap count) = (Nick''s lap count) + 4 Now that we have a "word equation" we need only fill in the missing information Marla completes 32 laps per hour We can ...” January 29, 2019 Brent@GMATPrepNow posted a reply to Paul, a painter, paints only flowers or cats in his notebook in the Data Sufficiency forum “I thought I''d point out that the approach demonstrated by Fabio and Jay is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of paintings, and the ...” January 29, 2019 Brent@GMATPrepNow posted a reply to f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. Wha in the Problem Solving forum “Given: f(x+y) = x + f(y) What is the value of f(100)? We need to somehow use the fact that f(0) = 5 to help us determine the value of f(100). Notice that we can rewrite 100 as 100 + 0 According to our the function f, we know that: f(100 + 0) = 100 + f(0) = 100 + 5 = 105 Answer: C ...” January 29, 2019 Brent@GMATPrepNow posted a reply to Leila is playing a carnival game in which she is given 4 in the Problem Solving forum “Given: P(succeeds on 1 throw) = 1/5 P(succeeds at least 3 times) = P(succeeds 4 times OR succeeds 3 times) = P(succeeds 4 times) + P(succeeds 3 times) P(succeeds 4 times) P(succeeds 4 times) = P(succeeds 1st time AND succeeds 2nd time AND succeeds 3rd time AND succeeds 4th time) = ...” January 29, 2019 Brent@GMATPrepNow posted a reply to A waitress's income consist of her salary and tips. During in the Problem Solving forum “APPROACH #1 - start with a convenient value of the server''s salary Let''s say her salary is$4 GIVEN: her tips were 5/4 of her salary 5/4 of $4 =$5 So, her tip total was $5 What fraction of her income for the week came from tips? Income = salary + tips =$4 + $5 =$9 Fraction = $5 /$9 ...”
January 29, 2019
Brent@GMATPrepNow posted a reply to To create a part for a certain piece of machinery, four equa in the Problem Solving forum
“IMPORTANT: the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise. We can use this fact to solve the question by simply "eyeballing" the diagram. The question is basically asking us to determine what percent of the circle is NOT shaded. Well, ...”
January 29, 2019
Brent@GMATPrepNow posted a reply to If (x+y)/z = -2, is x positive? in the Data Sufficiency forum
“Target question: Is x positive? Given: (x + y)/z = -2 Since the question asks about the variable x, let''s solve this equation for x. (x + y)/z = -2 So, x + y = -2z And, x = -2z - y This allows us to REPHRASE the target question.... REPHRASED target question: Is -2z - y positive? ...”
January 29, 2019
Brent@GMATPrepNow posted a reply to The table above shows the GPA of 20 students last semester. in the Problem Solving forum
“---------------ASIDE-------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”
January 28, 2019
Brent@GMATPrepNow posted a reply to A dental licensure exam requires a 75% minimum score in orde in the Data Sufficiency forum
“ Given: A dental licensure exam requires a 75% minimum score in order to pass each section Target question: Did Jennifer pass the 30-question third section? 75% of 30 = 22.5 So, in order to get at least 75% in the 3rd section, Jennifer must correctly answer 23 or more questions in the 3rd ...”
January 28, 2019
Brent@GMATPrepNow posted a reply to Barbara invests $2400 in the National Bank at 5%. How much in the Problem Solving forum “Barbara invests$2400 in the National Bank at 5%. So, her annual income for this investment = 5% of $2400 =$120 Let x = the additional money Barbara must invest at 8% So, her annual income for this investment = 8% of x = 0.08x So, Barbara''s TOTAL annual income = $120 + 0.08x We want the ...” January 27, 2019 Brent@GMATPrepNow posted a reply to A certain library assesses fines for overdue books as in the Problem Solving forum “1st day -$0.10 2nd day - $0.20 or$0.40 (double or add $0.30)$0.20 is the lesser amount 3rd day - $0.40 or$0.50 (double or add $0.30)$0.40 is the lesser amount 4th day - $0.80 or$0.70 (double or add $0.30)$0.70 is the lesser amount The correct answer is B Cheers, Brent”
January 27, 2019
Brent@GMATPrepNow posted a reply to Probability/ combination in the Problem Solving forum
“P(Tamara and Inga are BOTH chosen for the jury) = (# of ways to choose 7 people that include Tamara and Inga)/(TOTAL # of ways to choose 7 people) # of ways to choose 7 people that include Tamara and Inga Stage 1: place Tamara and Inga on the jury. This can be accomplished in 1 way Stage 2: ...”
January 26, 2019
Brent@GMATPrepNow posted a reply to A sports team played 100 games last season. Did this team in the Data Sufficiency forum
“Target question: Did this team win at least half of the games it played last season? Rephrased target question: Did this team win more than 49 games? Statement 1: The team won 60% of its first 65 games In other words, the team won 39 of its first 65 games Since we don''t know the results ...”
January 26, 2019
Brent@GMATPrepNow posted a reply to If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is in the Problem Solving forum
“GIVEN: the roots/solutions are x = -3 and x = 2 Notice that x = -3 and x = 2 are solutions to the equation (x + 3)(x - 2) = 0 If we expand and simplify the left side of the equation, we get: x² + x - 6 = 0 So, the equation x² + x - 6 = 0 has roots -3 and 2 Compare this to x² + px + q = 0 to ...”
January 25, 2019
Brent@GMATPrepNow posted a reply to The numbers m, n, and K are all positive integers. Given tha in the Problem Solving forum
“Different approach: The question asks "which of the following must also be a positive integer factor of K?" So, if we can find an answer choice that is NOT a factor of K we can ELIMINATE that answer choice. A. m + n If K = 12, then if COULD be the case that m = 4 and n = 6 In ...”
January 25, 2019
Brent@GMATPrepNow posted a reply to The numbers m, n, and K are all positive integers. Given tha in the Problem Solving forum
“GIVEN: m is a factor of K This means that we can write: K = md for some integer d If m and d are both integers, then m and d are both factors of K Notice that, if K = md, then d = K/m, which means K/m is a factor of K Answer: D Cheers, Brent”
January 25, 2019
Brent@GMATPrepNow posted a reply to If, J, K, L, M, and N are positive integers in ascending ord in the Data Sufficiency forum
“ Given: J, K, L, M, and N are positive integers in ascending order Target question: What is the value of L? Statement 1: The value of K is 3. There are many scenarios that satisfy statement 1. Here are two: Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the ...”
January 25, 2019
Brent@GMATPrepNow posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum
“To get a better idea of what''s happening, let''s sketch the set-up: https://i.imgur.com/SwHzFJD.png Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time. ...”
January 24, 2019
Brent@GMATPrepNow posted a reply to In the rectangular coordinate system above, the area of tria in the Problem Solving forum
“Let''s draw a rectangle around the triangle (as shown below) and then subtract from the rectangle''s area (28) the areas of the 3 right triangles that surround the triangle in question. We get the following: http://s13.postimage.org/a47qx0j8j/triangle_in_coordinate_plane_2.jpg So, the area ...”
January 24, 2019
Brent@GMATPrepNow posted a reply to A shirt that costs k dollars is increased by 30%, then by an in the Problem Solving forum
“A shirt that costs k dollars is increased by 30%, So, the new coast = k + (30% of k) = k + 0.3k = 1.3k ASIDE So, increasing a value by 30% is the same as multiplying that value by 1.3 Similarly, increasing a value by 20% is the same as multiplying that value by 1.2 And increasing a value by ...”
January 24, 2019
Brent@GMATPrepNow posted a reply to The total cost of a vacation was divided among 3 people. If in the Problem Solving forum
“Let T = total cost of vacation So, T/3 = cost per person with THREE people And T/4 = cost per person with FOUR people If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. In other words (cost per person with FOUR people) = ...” January 24, 2019 Brent@GMATPrepNow posted a reply to A restaurant meal cost$35.50 and there was no tax. If the t in the Problem Solving forum
“Let''s first see what happens when the tip is 10% 10% of $35.50 =$3.55 So, the total cost (WITH a 10% tip) = $35.50 +$3.55 = $39.05 So, the total cost must be GREATER THAN$39.05 This means the TOTAL cost could be $39.06 Check the answer choices.... A, D and E do not allow for the total cost ...” January 23, 2019 Brent@GMATPrepNow posted a reply to If i, a and b are integers, is 4(3b + 2) = 5a? (1) If i is in the Data Sufficiency forum “Target question: Is 4(3b + 2) = 5a? Statement 1: If i is divided by 5 the quotient is a and the remainder is 3 ASIDE: There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we ...” January 23, 2019 Brent@GMATPrepNow posted a reply to If the average of four numbers is 35, how many of the number in the Data Sufficiency forum “ Given: The average of four numbers is 35 Target question: How many of the numbers are less than 35? If we''re able to see that the statements FEEL insufficient, and we''re able to come up with some counter-examples in our head, then we can head straight to... . . . Statements 1 and 2 ...” January 23, 2019 Brent@GMATPrepNow posted a reply to If x is a positive integer, is x<16? 1) x is less than t in the Data Sufficiency forum “Target question: Is x < 16? Statement 1: x is less than the average (arithmetic mean) of the first ten positive integers Since the first ten positive integers are EQUALLY SPACED, the average = (smallest number + biggest number)/2 = (1 + 10)/2 = 5.5 So, x < 5.5 Since 5.5 < 16, we ...” January 23, 2019 Brent@GMATPrepNow posted a reply to What is the measure of each interior angle of a regular deca in the Problem Solving forum “Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180º) So, for example, the sum of the angles in an 11-sided polygon = (11 - 2)(180º) = (9)(180º) = 1620º What is the measure of each interior angle of a regular decagon? A decagon has 10 sides. The sum of the angles in ...” January 23, 2019 Brent@GMATPrepNow posted a reply to x=? in the Data Sufficiency forum “Target question: What is the value of x? Statement 1: x³ - x = 0 Factor to get: x(x² - 1) = 0 Factor again to get: x(x + 1)(x - 1) = 0 So, it could be the case that x = 0, x = -1 or x = 1 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT ...” January 23, 2019 Brent@GMATPrepNow posted a reply to Ayayai electronics is a company manufacturing MP3 players. in the Problem Solving forum “I thought I''d point out that Jay''s approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of MP3 players, and the two characteristics are: ...” January 23, 2019 Brent@GMATPrepNow posted a reply to If when a certain integer x is divided by 5, the remainder in the Problem Solving forum “Here''s another (longer) approach: When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k ...” January 22, 2019 Brent@GMATPrepNow posted a reply to If Polygon X has fewer than 9 sides, how many sides does in the Data Sufficiency forum “Target question: How many sides does Polygon X have? Given: Polygon X has fewer than 9 sides Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180º) Since the polygon has FEWER than 9 sides, there are are exactly SIX possible cases: case a: There are 8 sides, in ...” January 22, 2019 Brent@GMATPrepNow posted a reply to The number 75 can be written as the sum of the squares of 3 in the Problem Solving forum “We''re looking for 3 DIFFERENT squares that add to 75 Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64 Can you find 3 that add to 75? After some fiddling, we may notice that 1 + 25 + 49 In other words, 1² + 5² + 7² = 75 We want the SUM of 1 + 5 + 7, which is ...” January 22, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency Video #2: The Elimination Method Video: https://www.youtube.com/watch?v=amhxP9My_pU Cheers, Brent” January 22, 2019 Brent@GMATPrepNow posted a reply to The average salary of 15 people in the shipping department in the Problem Solving forum “]The average salary of 15 people in the shipping department at a certain firm is$20,000 So, (sum of all 15 salaries)/15 = $20,000 Multiply both sides by 15 to get: sum of all 15 salaries =$300,000 The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is$16,000 ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to A triangle has side lengths of a, b, and c centimeters. in the GMAT Math forum
“Target question: Does each angle in the triangle measure less than 90 degrees? Given: A triangle has side lengths of a, b, and c centimeters Statement 1: The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 cm², 4 cm², and 6 cm², respectively. ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to If x-2y=4, then x^2-4xy+4y^2-x+2y=? in the Problem Solving forum
“GIVEN: x - 2y = 4 We want to find the value of x² - 4xy + 4y² - x + 2y We should notice that x² - 4xy + 4y² is equal to (x - 2y)² We should notice that - x + 2y is equal to -(x - 2y) We get: x² - 4xy + 4y² - x + 2y = (x - 2y)² - (x - 2y) Now replace x - 2y with 4 to get: = (x - ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to What is the value of z in the triangle above? (1) x+y=139 ( in the Data Sufficiency forum
“Target question: What is the value of z in the triangle above? IMPORTANT: Since angles in a triangle must add to 180 degrees, we can write: x + y + z = 180 Statement 1: x + y = 139 Take: x + y + z = 180 and replace (x + y) with 139 to get: 139 + z = 180 Solve equation for z to get: z = 41 ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to 10 different biology books and 8 different chemistry books l in the Problem Solving forum
“Take the task of selecting 4 books and break it into stages. Stage 1: Select two biology books Since the order in which we select the books does not matter, we can use combinations. We can select 2 books from 10 books in 10C2 ways (45 ways) So, we can complete stage 1 in 45 ways If ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to What was the number of defective batteries in a shipment of in the Data Sufficiency forum
“Target question: What was the number of defective batteries in a shipment of 4000 batteries? Statement 1: In a particular sample of 10 batteries selected from the shipment, 1 was defective. Don''t make the mistake of assuming that this means 1/10 of ALL batteries are defective. There''s no ...”
January 21, 2019
Brent@GMATPrepNow posted a reply to On a game show, a contestant is given three keys, each of in the Problem Solving forum
“There aren''t many possible outcomes, so let''s start by listing all possibilities. Let A, B and C represent the 3 boxes, and let a, b, c, be the keys for those boxes (in that same order). A = $1 prize, B =$100 prize and C = $1000 prize If the boxes are arranged as A-B-C, then these are ...” January 20, 2019 Brent@GMATPrepNow posted a reply to Which of the following lists a number of points at which a in the Problem Solving forum “http://s27.postimg.cc/531tmnqpr/circ_int.jpg Answer: E The important takeaway here is that "intersect" does not necessarily mean "pass through" So, a line that is tangent to a circle (touching the circle but not passing through it) can be said to intersect the circle. To ...” January 20, 2019 Brent@GMATPrepNow posted a reply to [x] denotes the least integer greater than or equal to x ... in the Problem Solving forum “First, let''s take a moment to get a good idea of what this strange notation means. A few examples: -1 < x/2 ≤ 0 Multiply all sides of the inequality by 2 to get: -2 < x ≤ 0 Check the answer choices.... Only -3/2 falls inside that range. Answer: B Cheers, Brent” January 20, 2019 Brent@GMATPrepNow posted a reply to Full Plan in the The 60-Day GMAT Study Guide forum “Hi Aliya, I have a feeling that your email system is treating the emails as spam. Have you checked your spam/junk folders? You might to sign up for the emails again, but this time, be sure to add guide@beatthegmat.com as a contact in your e-mail system. This will help ensure that the daily ...” January 20, 2019 Brent@GMATPrepNow posted a reply to The average American spends y dollars on food per month, exc in the Problem Solving forum “This is a Variables in the Answer Choices question (VIAC). This question type can be answered algebraically or using the INPUT-OUTPUT approach. Mitch has demonstrated the INPUT-OUTPUT approach, so let''s solve the question algebraically. The average American spends y dollars on food per month, ...” January 20, 2019 Brent@GMATPrepNow posted a reply to If a is a positive integer and 81 divided by a in the Data Sufficiency forum “Target question: What is the value of a? Given: 81 divided by a results in a remainder of 1 In other words, 81 is 1 greater than some multiple of a This means that 80 is some multiple of a Another way to say this is: a is a divisor of 80 The divisors of 80 are: 1, 2, 4, 5, 8, 10, 16, ...” January 19, 2019 Brent@GMATPrepNow posted a reply to Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = th in the Problem Solving forum “Let''s list and count all possible outcomes. Possible products when 2 is selected from set A: 8, 10, 12, 14, 16 Possible products when 3 is selected from set A: 12, 15, 18, 21, 24 Possible products when 4 is selected from set A: 16, 20, 24, 28, 32 Possible products when 5 is selected from set ...” January 19, 2019 Brent@GMATPrepNow posted a reply to If Sam were twice as old as he is, he would be 40 years in the Problem Solving forum “Jim is 10 years younger than Sam Let x = Sam''s PRESENT age So, x - 10 = Jim''s PRESENT age If Sam were twice as old as he is, he would be 40 years older than Jim. TWICE Sam''s age = 2x So, we can write: 2x = (x - 10) + 40 Simplify: 2x = x + 30 Solve: x = 30 Answer: B Cheers, Brent” January 19, 2019 Brent@GMATPrepNow posted a reply to One night a certain hotel rented 3/4 of its rooms, including in the Problem Solving forum “This question is a great candidate for the Double Matrix method, whichcan be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of motel rooms, and the two characteristics are: - air conditioning or no air ...” January 19, 2019 Brent@GMATPrepNow posted a reply to In a certain pet shop, 1/3 of the pets are dogs and 1/5 of in the Data Sufficiency forum “Target question: How many of the pets are dogs? Given: 1/3 of pets are dogs & 1/5 of pets are birds Let T = TOTAL number of pets. So, T/3 = number of dogs And T/5 = number of birds Statement 1: There are 30 birds at the pet shop So, T/5 = 30 This means that T = 150, which ...” January 19, 2019 Brent@GMATPrepNow posted a reply to Is x > y? (1) -4x + 2y < y - 3x (2) wx > wy in the Data Sufficiency forum “Target question: Is x > y? Statement 1: -4x + 2y < y - 3x Add 4x to both sides to get: 2y < y + x Subtract y from both sides to get: y < x Perfect, the answer to the target question is YES, x IS greater than y Since we can answer the target question with certainty, statement 1 ...” January 19, 2019 Brent@GMATPrepNow posted a reply to At a certain fruit stand, the price of each apple is 40 cent in the Problem Solving forum “It turns out that the cost per apple is irrelevant. Here''s why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put ...” January 19, 2019 Brent@GMATPrepNow posted a reply to A set consists of 5 distinct positive integers a, b, c, d, e in the Problem Solving forum “The mean of all 5 numbers is 8.8 (a + b + c + d + e)/5 = 8.8 Multiply both sides by 5 to get: a + b + c + d + e = 44 The sum of a, c and e is 24 (a + c + e) = 24 So, take a + b + c + d + e = 44 and rewrite as: (a + c + e) + b + d = 44 We get: (24) + b + d = 44 So, b + d = 20 b is the ...” January 19, 2019 Brent@GMATPrepNow posted a reply to If x and y are consecutive integers such that x < y and x in the GMAT Math forum “Oops - pressed the wrong button. As you were! Brent” January 19, 2019 Brent@GMATPrepNow posted a reply to If 3 years ago Jennifer was 22 years old, how old is Carmen in the Data Sufficiency forum “Target question: How old is Carmen now? Given: 3 years ago Jennifer was 22 years old So, Jennifer''s PRESENT age is 25 Statement 1: 10 years ago, Carmen was twice as old as Jennifer. If Jennifer''s PRESENT age is 25, then Jennifer''s age 10 YEARS AGO was 15 This means Carmen''s age 10 ...” January 19, 2019 Brent@GMATPrepNow posted a reply to In a barrel full of apples, 45% of the apples weigh more in the Problem Solving forum “No takers? Let''s say there are 100 apples in the barrel. 45% of the apples weigh MORE THAN 81 grams This means 55% of the apples weigh LESS THAN OR EQUAL to 81 grams In other words, 55 apples weigh LESS THAN OR EQUAL to 81 grams 81% of the apples weigh LESS THAN 145 grams This means 19% ...” January 18, 2019 Brent@GMATPrepNow posted a reply to Passing the 30-question third section in the Data Sufficiency forum “ Given: A dental licensure exam requires a 75% minimum score in order to pass each section Target question: Did Jennifer pass the 30-question third section? 75% of 30 = 22.5 So, in order to get at least 75% in the 3rd section, Jennifer must correctly answer 23 or more questions in the 3rd ...” January 18, 2019 Brent@GMATPrepNow posted a reply to 32 teams compete in the World Cup of Soccer. They are divid in the Problem Solving forum “Perfect approach! ASIDE: We have 4 teams, and 2 teams play a game. So, the number of games played = the number of different ways to select 2 of the 4 teams = 4C2 = 6 Cheers, Brent” January 18, 2019 Brent@GMATPrepNow posted a reply to Does (a – 2)(b + 4) = 8? in the GMAT Math forum “Target question: Does (a – 2)(b + 4) = 8? This is a good candidate for rephrasing the target question. When I SCAN the statements, I see that statement 1 has the term ab. This suggests to me that we might benefit from EXPANDING the expression, since that will result in an ab term. Take: (a ...” January 18, 2019 Brent@GMATPrepNow posted a reply to A fair die has sides labeled with 1, 2, 3, 4, 5, and 6 dots. in the GMAT Math forum “We want P(select at least one 6) When it comes to probability questions involving "at least," it''s best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting at least one 6) = 1 - P(not getting at least one 6) What does ...” January 18, 2019 Brent@GMATPrepNow posted a reply to If x and y are consecutive integers such that x < y and x in the GMAT Math forum “GIVEN: x and y are consecutive integers such that x < y So, if x is ODD, then y is EVEN One option here is to replace the x''s and y''s with ODD and EVEN and apply the rules for ODDs and EVENs. Or we can just replace x and y with odd and even numbers. Let''s do that. Replace x with 1 ...” January 18, 2019 Brent@GMATPrepNow posted a reply to is x > 0? in the GMAT Math forum “Target question: Is x > 0 ? Statement 1: x – y > –8 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = 0. In this case, the answer to the target question is YES, x ...” January 18, 2019 Brent@GMATPrepNow posted a reply to If x is an integer greater than 2, the function f(x) in the GMAT Math forum “The key here is that f(51) is EQUAL to f(50) Here''s why: According to the definition of the function f, f(51) = (2)(4)(6). . . (48)(50), and f(50) = (2)(4)(6). . . (48)(50) So, f(51) - f(50) = (2)(4)(6). . . (48)(50) - (2)(4)(6). . . (48)(50) = 0 Answer: E Cheers, Brent” January 18, 2019 Brent@GMATPrepNow posted a reply to What percentage of his bills did Stanley pay before their in the Data Sufficiency forum “Target question: What percentage of his bills did Stanley pay before their due dates last month? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: Let P = # of bills PAID before due date Let T = TOTAL # of ...” January 17, 2019 Brent@GMATPrepNow posted a reply to Overlapping figures in the Problem Solving forum “If the area of the square is 4, then each side has length 2 https://i.imgur.com/Ul16WsZ.png At this point, we have a special 30-60-90 right triangle. When we compare this blue triangle to the BASE 30-60-90 right triangle . . . https://i.imgur.com/vrYSacE.png . . . we see that the blue ...” January 17, 2019 Brent@GMATPrepNow posted a new topic called Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = th in the Problem Solving forum “Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = the product of one number chosen from set A and one number chosen from set B, how many DIFFERENT values of P are possible? A) 14 B) 15 C) 16 D) 18 E) 20 Answer: C Difficulty level: 600 - 650 Source: www.gmatprepnow.com” January 17, 2019 Brent@GMATPrepNow posted a reply to If 20 Swiss Francs is enough to buy 9 notebooks in the Data Sufficiency forum “Target question: Is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? This is a great candidate for rephrasing the target question. Let N = the cost of 1 notebook (in Swiss francs) Let P = the cost of 1 pencil (in Swiss francs) So, 12 notebooks cost 12N and 12 pencils cost 12P ...” January 17, 2019 Brent@GMATPrepNow posted a reply to The speed of a boat is 5 times the speed at which a river fl in the Problem Solving forum “Let x = the speed of the river (in miles per hour) So, 5x = the speed of the boat in (miles per hour) Let d = distance traveled (in miles) This means the boat''s speed going UPriver = 5x - x = 4x And the boat''s speed going DOWNriver = x + 5x = 6x time = distance/speed So, travel time ...” January 17, 2019 Brent@GMATPrepNow posted a reply to If Jake loses 8 pounds, he will weigh twice as much as his s in the Problem Solving forum “Here''s a solution that uses one variable. Let x = Jake''s present weight in pounds So, x - 8 = Jake''s hypothetical weight IF he were to lose 8 pounds If Jake loses 8 pounds, he will weigh twice as much as his sister. In other words, the sister weighs HALF as much as Jake''s hypothetical ...” January 17, 2019 Brent@GMATPrepNow posted a reply to Three children, John, Paul, and Ringo, are playing a game. in the Problem Solving forum “The main concept here is that all 3 children are equally likely to win this game (unless one of them possesses supernatural powers that allow him to know what numbers the other two boys will choose :-)) Also note that, if everything is random, the probability of winning by choosing the number 2 ...” January 16, 2019 Brent@GMATPrepNow posted a new topic called In a barrel full of apples, 45% of the apples weigh more in the Problem Solving forum “In a barrel full of apples, 45% of the apples weigh more than 81 grams, and 81% of the apples weigh less than 145 grams. What percent of the apples in the barrel weigh more than 81 grams but less than 145 grams? A) 16 B) 18 C) 26 D) 32 E) 36 Answer: C Difficulty level: 600 - 650 Source: ...” January 16, 2019 Brent@GMATPrepNow posted a reply to What is the surface area of the solid right circular in the Problem Solving forum “Given: radius = 3 Height = 10 Surface area of cylinder = 2πr² + 2πrh = 2π(3²) + 2π(3)(10) = 18π + 60π = 78π Answer: D Cheers, Brent” January 16, 2019 Brent@GMATPrepNow posted a reply to Three children, John, Paul, and Ringo, are playing a game. in the Problem Solving forum “This is one of my all-time favorite questions!! The main concept here is that all 3 children are equally likely to win this game (unless one of them possesses supernatural powers that allow him to know what numbers the other two boys will choose :-)) Also note that, if everything is random, ...” January 16, 2019 Brent@GMATPrepNow posted a reply to GMAT Official Guide 2019 From 2000 to 2003, the number in the Problem Solving forum “From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4 Let x = the number of employees in 2000 So, the number of employees in 2003 = x + (1/4)x = (5/4)x From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3 (5/4)x = the ...” January 16, 2019 Brent@GMATPrepNow posted a reply to The usual price of a bagel was reduced during a sale. How mu in the Data Sufficiency forum “Target question: How much money could be saved by purchasing 10 bagels at the sale price rather than at the usual price? Statement 1: The usual price for a bagel is$0.50 per bagel. Since there''s no information about the SALE price, there''s no way to calculate the amount saved. Since we ...”
January 16, 2019
Brent@GMATPrepNow posted a reply to Henry eats X scones in X percent of the time it takes Rachel in the Problem Solving forum
“Let''s use the INPUT-OUTPUT approach. Let''s assign some values of X and Y so that they satisfy the information in the question. Let X = 25. This means Henry eats 25 scones in 25 percent of the time it takes Rachel to eat Y scones Let Y = 100. This means Henry eats 25 scones in 25 percent of ...”
January 15, 2019
Brent@GMATPrepNow posted a reply to Roger wants to arrange three of his five books on his in the Problem Solving forum
“I''m not crazy about this question. The official answer suggests that, although 2 books are DUPLICATES, they''re still considered DIFFERENT. Here''s what I mean: Let''s let D and d represent the two duplicate books. Let, A, B and C represent the other three books. The official answer ...”
January 15, 2019
Brent@GMATPrepNow posted a reply to The three-digit positive integer n can be written as ABC, in in the Data Sufficiency forum
“IMPORTANT point: The VALUE of a 3-digit integer xyz is 100x + 10y + z Example: 723 = (7)(100) + (2)(10) + 3 Target question: What is the remainder when n is divided by 37? Statement 1: A + B/10 + C/100 = B + C/10 + A/100 Multiply both sides by 100 to get: 100A + 10B + C = 100B + 10C + ...”
January 15, 2019
Brent@GMATPrepNow posted a reply to If x, y are integers, is x^2+x+y an odd integer? in the Data Sufficiency forum
“ Given: x and y are integers Target question: Is x² + x + y an odd integer? This is a good candidate for rephrasing the target question. Take x² + x + y and factor the first two terms to get: x(x + 1) + y Notice that x and x+1 are CONSECUTIVE INTEGERS, which means one value is ODD and ...”
January 15, 2019
Brent@GMATPrepNow posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”
January 15, 2019
Brent@GMATPrepNow posted a reply to Three machines have equal constant work rates. It takes h + in the Problem Solving forum
“ It takes h + 3 hours to produce 360 toys when 2 machines work together So, during those h + 3 hours, EACH machine makes 180 toys So, ONE machine can produce 180 toys in h + 3 hours rate = output/time So, we can write: rate of ONE machine = 180/(h + 3) It takes h hours to produce 360 toys ...”
January 14, 2019
Brent@GMATPrepNow posted a reply to There is a total of 120 marbles in a box, each of which is in the Problem Solving forum
“...the probability that it So, 1/4 of the 120 marbles are white. In other words, there are 30 white marbles. ...the probability that it So, 1/3 of the 120 marbles are green . In other words, there are 40 green marbles. Altogether, there are 70 marbles that are EITHER white or green. ...”
January 12, 2019
Brent@GMATPrepNow posted a reply to To furnish a room in model home, an interior decorator is to in the Problem Solving forum
“Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables) So, 150 = (# of ways to select 2 chairs)(# of ways to select 2 tables) # of ways to select 2 chairs 5 tables, choose 2 of them. Since the order of the selected chairs does not matter, we can use ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to At a certain fruit stand, the price of each apple is 40 in the Problem Solving forum
“It turns out that the cost per apple is irrelevant. Here''s why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to A librarian has a set of ten books, including four different in the Problem Solving forum
“Take the task of arranging the 10 books and break it into stages. Stage 1: Arrange the 4 books about Abe Lincoln in a row We can arrange n objects in n! ways. So, we can arrange the 4 books in 4! ways IMPORTANT: Now we''ll "glue" the 4 Abe Lincoln books together to form 1 SUPER ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to By what percent is 25 greater than 15? in the Problem Solving forum
“An alternative approach is to test the answer choices First, however, we can eliminate some answer choices by first testing an easy value: 50% Is 25 50% greater than 15? Well, 50% of 15 = 7.5 So, 50% greater than 15 = 15 + 7.5 = 22.5 22.5 is too small (we need to get 25), so we need a ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum
“Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs $2.90 We can write: C + 10M = 2.90 A 16-minute call costs$4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to At the end of the first quarter, the share price of a in the Problem Solving forum
“Let $100 = share price at the beginning of the year At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. So,$120 = share price at the end of the first quarter At the end of the second quarter, the share ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency Video #1: Introduction to GMAT Data Sufficiency Video: https://www.youtube.com/watch?v=3MaEqnSnK-s Cheers, Brent”
January 10, 2019
Brent@GMATPrepNow posted a reply to 17^27 has a units digit of: in the Problem Solving forum
“Look for a pattern 17^1 = 17 17^2 = (17)(17) = ---9 17^3 = (17)(17^2) = (17)(---9) = ----3 17^4 = (17)(17^3) = (17)(---3) = ----1 17^5 = (17)(17^4) = (17)(---1) = ----7 NOTICE that we''re back to where we started. 17^5 has units digit 7, and 17^1 has units digit 7 So, at this point, ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to The water from one outlet, flowing at a constant rate, can f in the Problem Solving forum
“One approach is to assign a NICE NUMBER to the volume of the swimming pool. This number will work well with the two pieces of information (fill pool in 9 hours and fill pool in 5 hours). So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant ...”
January 9, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive, is x > y? in the Data Sufficiency forum
“Target question: Is x > y? This is a good candidate for rephrasing the target question. Since y is POSITIVE, we can safely take the inequality x > y and divide both sides by y to get: x/y > 1 REPHRASED target question: Is x/y > 1? Aside: Here’s a video with tips on rephrasing ...”
January 9, 2019
Brent@GMATPrepNow posted a reply to Emily keeps 12 different pairs of shoes (24 individual shoes in the Problem Solving forum
“P(dog selects matching pair) = P(dog chooses ANY sock 1st AND 2nd sock matches the 1st sock) = P(dog chooses ANY sock 1st) x P(2nd sock matches the 1st sock) = 24/24 x 1/23 = 1/23 Answer: C Cheers, Brent”
January 9, 2019
Brent@GMATPrepNow posted a reply to On a certain Monday, Carlos drove to work at an average in the Problem Solving forum
“Average speed = (TOTAL distance)/TOTAL travel time)Carlos drove to work at an average speed of 50 miles per hour Time = distance/speed So, travel time TO work = d/50 hours Carlos drove home from work at an average speed of 70 miles per hour So, travel time FROM work = d/70 hours So, TOTAL ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to How many integers between in the Problem Solving forum
“He spent 40% (of the $35) on chicken feed. 40% of$35 = $14. So, he spent$14 on chicken feed. He got a 20% discount on the chicken feed. In other words, he paid 80% of the original price. So, let C = original price of chicken feed. We can write 80% of C = $14 Or we can write 0.8C =$14 ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to On Monday, the opening price of a certain stock was $100 in the Problem Solving forum “On Monday, the opening price of a certain stock was$100 per share and its closing price was $110 per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, We can say that the stock LOST 10% of its value. OR we can say that the stock RETAINED 90% ...” January 8, 2019 Brent@GMATPrepNow posted a reply to A department manager distributed a number of pens, pencils, in the Data Sufficiency forum “Jay''s solution is great. I just wanted to mention that this question hinges largely on the fact that the number of pens, pencils, and pads that each staff member receives MUST HAVE INTEGER VALUES. So, for example, if statement 1 were different and statement 2 read "The manager ...” January 8, 2019 Brent@GMATPrepNow posted a reply to In 1982 and 1983, Company B's operating expenses were$12.0 in the Problem Solving forum
“The profit in 1982 = 15.6 - 12.0 = $3.6 million The profit in 1983 = 18.8 - 14.0 =$4.8 million Percent change = (100)(new - old)/old = (100)(4.8 - 3.6)/3.6 = (100)(1.2)/(3.6) = (100)(1/3) = 33 1/3% Answer: D Cheers, Brent”
January 8, 2019
Brent@GMATPrepNow posted a reply to x is a positive integer, and the units digits of both (x+2)^ in the Problem Solving forum
“Another approach is to test the answer choices A. If the units digit of x is 1, is it the case that units digits of both (x+2)² and (x-2)² is 9? Well, (x+2)² = (1+2)² = 9. Works! To test (x-2)², let''s let x = 11. We get: (11-2)² = 9² = 81. NO GOOD ELIMINATE A B. If the units digit ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to In 1991, the price of a house was 80% of its original price. in the Problem Solving forum
“I''d typically assign a "nice" value to the original price, and then follow the steps that Mitch demonstrated. Alternatively, we can solve the question algebraically In 1991, the price of a house was 80% of its original price. Let x = the original price So, 0.8x = the 1991 price ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to If triangle ABC is an isosceles triangle, what is ∠ABC? in the Data Sufficiency forum
“Target question: What is ∠ABC? Given: Triangle ABC is an isosceles triangle So, ∆ABC has 2 equal angles Statement 1: ∠CAB = 45 degrees Since ∆ABC has 2 equal angles, there are two possible triangles that satisfy statement 1: Case a: ∠CAB = 45, ∠BCA = 45 and ∠ABC = 90. ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to If f(a*b) = f(a) + f(b), what is the value of f(1)? in the Problem Solving forum
“To generalize Mitch''s and Fabio''s solutions, notice that, as long as we can get f(1) involved in the process, we''ll arrive at answer choice C every time. Notice that k = 1*k Since f(a*b) = f(a) + f(b), we can write: f(1*k) = f(1) + f(k) Simplify: f(k) = f(1) + f(k) Subtract f(k) from both ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to After her birthday, Fiona had D dollars in gift money. in the Problem Solving forum
“Another approach is to use algebra. After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard. If Fiona SPENT 3/5 of D dollars, then 2/5 of D dollars REMAINED In other words, the amount remaining at the end of the day = 2D/5 dollars The next day, ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to After her birthday, Fiona had D dollars in gift money. in the Problem Solving forum
“One option is to WORK BACKWARDS The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank. If she spent 1/3 of her money on a movie passcard, then 2/3 of her money remained (which she put in the bank). This means 2/3 of her money =$80 We ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to A retailer sells only radios and clocks. If she currently ha in the Data Sufficiency forum
“ Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory. Target question: How many radios are there in the inventory Statement 1: The retailer has more than 28 radios in inventory There are several scenarios that satisfy statement 1. Here are ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to Number Properties in the Data Sufficiency forum
“The error is highlighted above in blue. if a>0 we will have the answer as YES is ALMOST true. The only time it''s not true is when a = 1 If a = 1, then the answer is NO. We can verify this using either the original inequality or the rephrased inequality. Take "Is a + 1/a > ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to A store sells erasers for 0.23$per piece and pencil for in the Data Sufficiency forum “This question illustrates a common trap on the GMAT. As Jay has shown, with statement 2, we''re able to write the equation 23x + 11y = 170 , and in high school we learned that, if we''re given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the ...” January 5, 2019 Brent@GMATPrepNow posted a reply to A barn is enclosed in the shape of a 6-sided figure; all in the Data Sufficiency forum “This Date Sufficiency question is almost identical to the following Problem Solving question, which requires us to find the actual area: http://www.beatthegmat.com/plz-explain-t270003.html Cheers, Brent” January 5, 2019 Brent@GMATPrepNow posted a reply to In the rectangular coordinate system above, the area of in the Problem Solving forum “Let''s draw a rectangle around the triangle (as shown below) and then subtract from the rectangle''s area (28) the areas of the 3 right triangles that surround the triangle in question. We get the following: http://s13.postimage.org/a47qx0j8j/triangle_in_coordinate_plane_2.jpg So, the area ...” January 5, 2019 Brent@GMATPrepNow posted a reply to What is the perimeter of quadrilateral Q? in the Data Sufficiency forum “Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...” January 5, 2019 Brent@GMATPrepNow posted a reply to The price of a consumer good increased by p% in the Problem Solving forum “Let$100 be the original price The price of a consumer good increased by p% during 2012 p% = p/100, so a p% INCREASE is the same a multiplying the original price by 1 + p/100 So, the new price = ($100)(1 + p/100) The price then decreased by 12% during 2013 A 12% DECREASE is the same a ...” January 5, 2019 Brent@GMATPrepNow posted a reply to The number of students who attend a school could be divided in the Problem Solving forum “The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. This tells us that the TOTAL number of students is a multiple of 10, 12 and 16 What is the minimum number of students that could attend the school? ...” January 5, 2019 Brent@GMATPrepNow posted a reply to Set K consists of a finite number of consecutive odd in the Data Sufficiency forum “Target question: What is the value of y - x? Given: Set K consists of a finite number of consecutive odd integers Statement 1: The average (arithmetic mean) of set K is –36 There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the ...” January 5, 2019 Brent@GMATPrepNow posted a reply to The value of (10^8-10^2)/(10^7-10^3) is closest to which in the Problem Solving forum “Since the answer choices are so spread out, we can be quite aggressive with out estimation. First, 10⁸ - 10² can be rounded to 10⁸ Is this reasonable? Well, 10⁸ equals 100,000,000, so subtracting 10² (aka 100) from 100,000,000 still leaves us with approximately 100,000,000 ...” January 5, 2019 Brent@GMATPrepNow posted a reply to Each of the 25 balls in a certain box is either red, blue, in the Data Sufficiency forum “Target question: What is the value of P(white or even)? To solve this, we need P(A or B) = P(A) + P(B) - P(A & B) So, P(white or even) = P(white) + P(even) - P(white & even) Statement 1: P(white & even) = 0 We can add this to our probability equation to get: P(white or even) = ...” January 4, 2019 Brent@GMATPrepNow posted a reply to The profit from the sale of a certain appliance increases, in the Data Sufficiency forum “Target question: Did the profit exceed$4 million on sales of 380,000 units? Given: The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. IMPORTANT: This means that we CANNOT make any "good" assumptions about the ...”
January 4, 2019
Brent@GMATPrepNow posted a reply to If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? in the Problem Solving forum
“Given: y = 2 + 2k Rewrite as: y/1 = (2 + 2k)/1 Flip both fractions to get: 1/y = 1/(2 + 2k) So, 1/y + 1/y + 1/y + 1/y = 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) = 4/(2 + 2k) = 4/(2)(1 + k) = 2/(1 + k) Answer: B Cheers, Brent”
January 4, 2019
Brent@GMATPrepNow posted a reply to Is x/y < 0? in the Data Sufficiency forum
“Target question: Is x/y < 0? Statement 1: (x^4)(y^5) < 0 There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = -1. Notice that (x^4)(y^5) = (1^4)(-1^5) = (1)(-1) = -1, which is less than 0. In this case, x/y = 1/(-1) = -1. So, the answer to ...”
January 4, 2019
Brent@GMATPrepNow posted a reply to If 4+ 1n = 55n, what is the value of n? in the Problem Solving forum
“GIVEN: √(4 + 1/n) = 5√(5/n) Square both sides to get: (5)(5)√(5/n)√(5/n) Simplify right side again: 4 + 1/n = 25(5/n) Simplify right side: 4 + 1/n = 125/n Multiply both sides by n to get: 4n + 1 = 125 Subtract 1 from both sides to get: 4n = 124 Solve: n = 124/4 =31 Answer: A ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to On a construction site, 16 of the men wear helmets, and 19 in the Data Sufficiency forum
“I thought I''d point out that Jay''s approach is also known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of construction worker, and the two ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to If the average of four numbers is 35, how many of the in the Data Sufficiency forum
“Target question: How many of the numbers are less than 35? Given: The average of four numbers is 35 All this tells us is that the SUM of the 4 numbers is 140 (since 140/4 = 35) Given the limited amount of information, it''s likely that the correct answer is C or E Statement 1: None of ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to Absolute value in the Problem Solving forum
“A quick approach is to simply test the answer choices A) -2 No good. The absolute value of something cannot be negative B) 0 Plug in to get |0² - 6| = 0. Doesn''t work. C) 1 Plug in to get |1² - 6| = 1. Doesn''t work. D) 3 Plug in to get |3² - 6| = 3. WORKS!!! Answer: D Cheers, ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to If m and n are positive integers such that m>n, what is t in the Data Sufficiency forum
“ Given: m and n are positive integers such that m > n Target question: What is the remainder when m² – n² is divided by 21? Statement 1: The remainder when (m + n) is divided by 21 is 1 There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 12 and ...”
January 2, 2019
Brent@GMATPrepNow posted a reply to If x + y is not equal to 0. What is the value of (ax + ay)/( in the Data Sufficiency forum
“Target question: What is the value of (ax + ay)/(x + y)? This is a good candidate for rephrasing the target question. Take the expression: (ax + ay)/(x + y) Factor the numerator to get: a(x + y)/(x + y) Simplify the fraction to get: a Since (ax + ay)/(x + y) = a, we can rephrase the target ...”
January 2, 2019
Brent@GMATPrepNow posted a reply to Can n be expressed as the difference of 2 prime numbers? in the Data Sufficiency forum
“Target question: Can n be expressed as the difference of 2 prime numbers? Statement 1: (n-17)(n-21) = 0 This tells us that EITHER n = 17 OR n = 21 IMPORTANT: Upon seeing that n can equal one of two values, some students will incorrectly conclude that statement 1 is not sufficient. However, ...”
January 2, 2019
Brent@GMATPrepNow posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”
January 1, 2019
Brent@GMATPrepNow posted a reply to What is the value of the integer n? in the Data Sufficiency forum
“Target question: What is the value of the integer n? Statement 1: n is a prime factor of 21 21 = (3)(7) So, EITHER n = 3 OR n = 7 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: n is a factor of 49 49 has three positive factors: 1, ...”
January 1, 2019
Brent@GMATPrepNow posted a reply to If 2x+y=3 and 4x^2-4xy+y^2=1, what is the value of xy? in the Problem Solving forum
“This question becomes a lot easier if we recognize that (2x + y)² = 4x² + 4xy + y² (which is VERY similar to 4x² - 4xy + y²) Here''s what I mean: Take 2x + y = 3 and square both sides to get: (2x + y)² = 3² Simplify both sides to get: 4x² + 4xy + y²= 9 We now have two (quite ...”
January 1, 2019
Brent@GMATPrepNow posted a reply to Given four rods of length 1 meter, 3 meters, 5 meters, and 7 in the Problem Solving forum
“IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . . DIFFERENCE between A and B < length of third side < SUM of A and B Let''s focus on this part: length of third side < SUM of A and B We can also say that the length of LONGEST side must be less than the SUM of ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to Brady, Charlie, and Daryl play on the same baseball team. Th in the Data Sufficiency forum
“ Given: Brady, Charlie, and Daryl play on the same baseball team. Target question: The number of home runs hit by Brady in a particular season is what fraction of the total home runs hit by the three players in that season? This is a good candidate for rephrasing the target question. Let ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to What is the 1st term in sequence S ? (1) The 3rd term in S in the Data Sufficiency forum
“Target question: What is the 1st term in sequence S ? Statement 1: The 3rd term in S is 2 Since we''re not given any information about the NATURE of the sequence, there''s no way to answer the target question with certainty. So, statement 1 is NOT SUFFICIENT Statement 2: The 2nd term in ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Here''s our video on Weighted Averages video: https://www.youtube.com/watch?v=B7J6lr_qBG4 Cheers, Brent”
December 31, 2018
Brent@GMATPrepNow posted a reply to Marcia's bucket can hold a maximum of how many liters of wat in the Data Sufficiency forum
“Target question: Marcia''s bucket can hold a maximum of how many liters of water? In other words, what is the TOTAL CAPACITY of Marcia''s bucket? Statement 1: The bucket currently contains 9 liters of water. Not enough info to determine the TOTAL CAPACITY of Marcia''s bucket. Since we ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to In a stack of boards at a lumber yard, the 20th board counti in the Problem Solving forum
“Let''s start from the bottom and work our way up: We''ll start with the 16th board counting from the bottom of the stack Right BELOW that 16th board, we have a board that we''ll call Larry. So, Larry is the 15th board counting from the bottom of the stack. So, starting from the bottom and ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to Overlapping Sets in the Data Sufficiency forum
“I thought I''d point out that Manasa3190''s approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of people, and the two characteristics are: ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to Car X left Town T (RATE PROBLEM, Need Help) in the Problem Solving forum
“IMPORTANT: Let''s use HOURS throughout our solution, and then convert hours to minutes at the end. When car Y had traveled for z HOURS, car Y had traveled 23 miles more that car X had from the time that car X left Town T. z = car Y''s travel time in HOURS So, z + 3/10 = car X''s travel time in ...”
December 28, 2018
Brent@GMATPrepNow posted a reply to A shipping company has four empty trucks that will head out in the Problem Solving forum
“Take the task of shipping the 4 boxes and break it into stages. Let''s call the 4 boxes A, B, C and D Stage 1: Select a truck to ship box A in There are 4 trucks from which to choose, so we can complete stage 1 in 4 ways Stage 2: Select a truck to ship box B in There are 4 trucks ...”
December 24, 2018
Brent@GMATPrepNow posted a reply to resolution in the Data Sufficiency forum
“ Given: A quorum of at least half the 20 directors must pass the resolution by at least a two-thirds majority Target question: At a meeting of the board of directors, did resolution X pass or fail?  Statement 1: Ten directors voted for the resolution.  KEY: We don''t know how many ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to a data from gmat forum in the Data Sufficiency forum
“ Given: Every student at the Performing Arts Academy must take at least one of the two drama courses offered, Classical Theater or Improvisation. 15% of the students who take Classical Theater also take Improvisation Let''s use the Every student at the Performing Arts Academy must take at least ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to Tough Rate problem in the Data Sufficiency forum
“ Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour? Statement 1: Each person in ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to Two trees have a combined height of 60 feet, and the taller in the Problem Solving forum
“Let y = the height of the shorter tree The taller tree is x times the height of the shorter tree. Ho So, yx = the height of the taller tree The two trees have a combined height of 60 feet We can write: y + yx = 60 How tall is the shorter tree, in terms of x? We must solve the equation ...”
December 22, 2018
Brent@GMATPrepNow posted a reply to Two water pumps, working simultaneously at their respective in the Problem Solving forum
“Let''s pick some nice numbers that adhere to the given information. ...the constant rate of one pump was 1.5 times the constant rate of the other So, the fast pump has a pumping rate that''s 1.5 faster then the slow pump. So, let''s say the SLOW pump pumps at 2 gallons per hour This means ...”
December 22, 2018
Brent@GMATPrepNow posted a reply to Fractions/Ratios in the Data Sufficiency forum
“ Given: There are two types of rolls on a counter, plain rolls and seeded rolls. Let P = # of plain rolls Let S = # of seeded rolls Target question: What is the value of P + S? Statement 1: The ratio of the number of seeded rolls on the counter to the number of plain rolls on the ...”
December 21, 2018
Brent@GMATPrepNow posted a reply to Five friends - Ross, Phoebe, Chandler, Joey and Monica - in the Problem Solving forum
“Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...”
December 21, 2018
Brent@GMATPrepNow posted a reply to A list kept at Town Hall contains that town's average daily in the Data Sufficiency forum
“Target question: Does this month have 30 or 31 days? IMPORTANT: Notice that the question does not ask "How many days are in this month?" If that were the case, then we''d have to consider February. Instead, the question is ruling out February by basically telling us that the month in ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to In how many ways can the letters D, I, G, I, T be arranged in the Problem Solving forum
“One approach is to count all possible arrangements (that may or may not break the given rule) and then subtract all outcomes the break the rule. Here''s another approach. Take the task of arranging the 5 letters and break it into stages. Stage 1: Arrange the 3 CONSONANTS (D, G and T) in a ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to Inequalities in the GMAT Math forum
“Target question: Is x² > y²? Statement 2: x > y There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 2 and y = 1. In this case, x² = 4 and y² = 1. So, the answer to the target question is YES, x² IS greater than y² Case b: x = -2 and y = -3. ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum
“Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to Two dice, each with six sides numbered 1 through 6, are toss in the Problem Solving forum
“P(both dice will come up with either a 1 or a 2) = P(1st die is 1 or 2 AND 2nd die is 1 or 2) = P(1st die is 1 or 2) x P(2nd die is 1 or 2) = 2/6 x 2/6 = 1/3 x 1/3 = 1/9 Answer: C Cheers, Brent”
December 20, 2018
Brent@GMATPrepNow posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom apart in the Problem Solving forum
“A fast and easy approach is to assign a "nice" value to the monthly rent of a ONE-bedroom apartment. Let''s say the rent on a ONE-bedroom apartment is $100 per month A two-bedroom apartment costs 50% more to rent than a one-bedroom apartment 50% of$100 = $50 So, the rent on a ...” December 20, 2018 Brent@GMATPrepNow posted a reply to If the remainder when positive integer x is divided by 7 is in the Data Sufficiency forum “Target question: What is the value of x? Given: If the remainder when positive integer x is divided by 7 is 4 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For ...” December 20, 2018 Brent@GMATPrepNow posted a reply to The value of a share was 25% less in the 2nd quarter over in the Problem Solving forum “Let''s assign a nice value to the share value in the 1st quarter. Let''s say the share value in the 1st quarter =$100 The value of a share was 25% less in the 2nd quarter over the 1st quarter . . . So, the share value in the 2nd quarter = $100 - (25% of$100) = $100 -$25 = $75 . . . ...” December 20, 2018 Brent@GMATPrepNow posted a reply to The usual price of a bagel was reduced during a sale. How in the Data Sufficiency forum “Target question: How much money could be saved by purchasing 10 bagels at the sale price rather than at the usual price? Statement 1: The usual price for a bagel is$0.50 per bagel. Since there''s no information about the SALE price, there''s no way to calculate the amount saved. Since we ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to One woman and one man can build a wall together in two hours in the Problem Solving forum
“One approach is to determine the size of the job One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. The part in blue tells us that 2 girls have the same output as 1 man. ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 in the Data Sufficiency forum
“When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Target question: Is x > 0 ? Statement 1: |x+3| < ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to In the xy-plane, what is the y-intercept of line l? in the Data Sufficiency forum
“Target question: What is the y-intercept of line L? IMPORTANT: When I scan the two statements, I see that they are strongly related. If the x-intercept is -1/3 (as per statement 2), the slope of the line is GUARANTEED to be 3 times its y-intercept (as per statement 1). Here''s why... ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to At garage sale, all of the prices of the items sold were in the Problem Solving forum
“The price of the radio was the 15th highest price So, there were 14 items that were more expensive than the radio. In other words, if we listed all of the prices in ascending order, we''d get something like: ........... radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X The price of the radio ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to A certain company charges $6 per package to ship packages in the Problem Solving forum “Let x = the weight of the package (in pounds) So, the shipping cost =$6 + 2x We''re told the shipping cost is \$38. So, we can write: 6 + 2x = 38 Subtract 6 from both sides: 2x = 32 Solve: x = 32/2 = 16 Answer: A Cheers, Brent”
December 19, 2018
Brent@GMATPrepNow posted a reply to Is x/y>1? in the Data Sufficiency forum
“Target question: Is x/y > 1? Statement 1: x > y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is YES, x/y IS greater than 1 Case b: x = ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to How many 4-digit numbers greater than 3,000 have the digits: in the Problem Solving forum
“Take the task of creating 4-digit numbers and break it into stages. We’ll begin with the most restrictive stage. Stage 1: Select the first digit (to go in the thousands place) Since the 4-digit number must be GREATER THAN 3000, the first digit must be greater than or equal to 3 This means ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
December 18, 2018
Brent@GMATPrepNow posted a reply to At a certain university, the ratio of the number of teaching in the Problem Solving forum
“We can solve this using equivalent ratios We''re comparing teaching assistants/number of students Let x = number of students possible We can write: 5/x = 3/80 Cross multiply to get: 3x = (5)(80) Simplify: 3x = 400 Solve: x = 400/3 = 133 1/3 = 133.3333 Since 134 students would exceed ...”
December 18, 2018
Brent@GMATPrepNow posted a reply to Automobile A is traveling at two-thirds the speed that in the Data Sufficiency forum
“ Given: Automobile A is traveling at two-thirds the speed that Automobile B is traveling. Let A = Car A''s speed Let B = Car B''s speed So, we can write: A = (2/3)B Target question: What is the value of A? Statement 1: If both automobiles increased their speed by 10 miles per hour, ...”
December 18, 2018
Brent@GMATPrepNow posted a reply to If every boy in a kindergarten class buys a soda and every g in the Problem Solving forum
“Let B = # of boys in kindergarten Let G = # of girls in kindergarten Let J = price (in CENTS) of ONE juice box Let S = price (in CENTS) of ONE soda If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“You could also try testing the answer choices. Cheers, Brent”
December 17, 2018
Brent@GMATPrepNow posted a reply to If 3x + 12 = 21, then x + 4 = A. 3 B. 4 C. 5 D. 7 E. 9 in the Problem Solving forum
“One option is to first solve the equation, 3x + 12 = 21, for x, and then determine the value of x+4. Alternatively, we can factor the left side to get: 3(x + 4) = 21 Now divide both sides by 3 to get: x + 4 = 7 Answer: D Cheers, Brent”
December 17, 2018
Brent@GMATPrepNow posted a reply to If a, b & c are integers, is abc odd? in the Data Sufficiency forum
“Some important rules: #1. (ODD)(ODD) = ODD #2. (ODD)(EVEN) = EVEN #3. (EVEN)(EVEN) = EVEN Given: a, b & c are integers Target question: Is abc odd? Statement 1: ab is odd This tells us that a and b are both odd. However, we have no information about c. Consider these two ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to In the coordinate plane, the y-intercept of the line k is eq in the Problem Solving forum
“One approach is to choose some values that meet the given information. In the coordinate plane, the y-intercept of the line k is equal to twice its slope. Okay, so let''s say the y-intercept of line k is 6. We get: https://i.imgur.com/qJ5GeRQ.png Since the y-intercept (6) is TWICE the ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“Let''s start with a "Word Equation" (distance traveled uphill) + (distance traveled downhill) = TOTAL DISTANCE Let t = the time spent jogging UPHILL (in hours) The total travel time = 40 minutes = 2/3 HOURS So, 2/3 - t = the time spent jogging DOWNHILL (in hours) Distance = ...”
December 16, 2018