Ian Stewart posted a reply to What is the value of y? in the Data Sufficiency forum
“Each statement is clearly insufficient alone. Using both, from Statement 1 we can factor since we have a difference of squares: (x + y)(x - y) = 5 From Statement 2, x+y and x-y are both integers, and if x and y are each positive integers, x+y is greater than 1. Since x+y is also clearly a ...”
Yesterday
Ian Stewart posted a reply to In the rectangular coordinate system shown above, does the in the Data Sufficiency forum
“If a line has a negative slope, that line is falling as it moves to the right. So it is rising as it moves to the left, and eventually it will rise high enough to be in quadrant II. So Statement 1 is sufficient. Statement 2 tells us one point on the line but nothing about how the line rises or ...”
Yesterday
Ian Stewart posted a reply to An art gallery has only paintings and sculptures. Currently, in the Problem Solving forum
“If 1/3 of the non-displayed things are paintings, 2/3 of them are sculptures. So if 200 are sculptures, we have 300 non-displayed things in total. Since 1/3 of things are on display, the ratio of displayed to not is 1 to 2, so we have 150 things on display, and 150+300 = 450 things in total.”
Yesterday
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
GMATGuruNY posted a reply to (n+1)!f(n) = (n-1)!. What is the value of f(1) + f(2) + … in the Problem Solving forum
“f(n) = (n-1)!/(n+1)! f(1) = 0!/2! = 1/2 f(2) = 1!/3! = 1/6 f(3) = 2!/4! = 1/12 f(4) = 3!/5! = 1/20 f(1) + f(2) = 1/2 + 1/6 = 2/3 f(1) + f(2) + f(3) = 2/3 + 1/12 = 3/4 f(1) + f(2) + f(3) + f(4) = 3/4 + 1/20 = 4/5 The sum of the first 2 terms = 2/3. The sum of the first 3 terms = 3/4. ...”
May 17, 2019
GMATGuruNY posted a reply to A 3-digit positive integer consists of non zero digits. If in the Problem Solving forum
“Alternate approach: Integers with exactly 2 digits the same = Total integers - Integers with all 3 digits the same - Integers with all 3 digits different. Total integers: Number of options for the hundreds digit = 9. (Any digit but 0.) Number of options for the tens digit = 9. (Any digit ...”
May 16, 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
GMATGuruNY posted a reply to What is the value of x? in the Data Sufficiency forum
“Statement 1: Squaring both sides, we get: x² + y² + 2xy = x² + y² - 2xy 4xy = 0 xy = 0 Case 1: x=0, with the result that y can be any value Case 2: y=0, with the result that x can be any value Since Case 2 allows x to be any value, INSUFFICIENT. Statement 2: Here, y can be any ...”
May 16, 2019
GMATGuruNY posted a reply to Each of A, B and C represents a one-digit integer. AB and BA in the Problem Solving forum
“325 = 100*3 + 10*2 + 5 648 = 100*6 + 10*4 + 8 Generally: Three-digit integer XYZ = 100X + 10Y + Z Since BA + AB + AB = CAA, we get: (10B+A) + (10A+B) + (10A+B) = 100C + 10A + A 12B + 21A = 100C + 11A 12B + 10A = 100C 12B + 10A = MULTIPLE OF 100 Since B and A are digits, the left side will ...”
May 16, 2019
GMATGuruNY posted a reply to The federal immigration station on Ellis Island - GMATPrep in the Sentence Correction forum
“Yes. E: Of all immigrants...the station processed nearly three quarters of them. Here, the red modifier is redundant with the blue modifier. Generally, COMMA + having + VERBed serves to express an action that happens before the action in the preceding clause. E: The federal immigration ...”
May 15, 2019
Ian Stewart posted a reply to The age of a group of people follows a distribution, which in the Problem Solving forum
“95% of the distribution is within two standard deviations of the mean, so 95% of the distribution lies between A - 2SD and A + 2SD. So all of those values are less than A+2SD. The other 5% of the distribution is more than two standard deviations from the mean. Since the distribution is symmetric, ...”
May 15, 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
GMATGuruNY posted a reply to In the xy-coordinate system, rectangle ABCD is inscribed in the Problem Solving forum
“x²+y² = r² is the equation for a circle with its center at the origin and a radius of r. Thus, x²+y² = 25 is a circle with a center at the origin and a radius of 5. The information in the prompt yields the following figure: https://i.postimg.cc/xJCgjxbd/rectangle-in-circle.png OB is a ...”
May 15, 2019
Ian Stewart posted a reply to The median of n consecutive odd integers is 30. If the fifth in the Problem Solving forum
“This question makes no sense - they are misusing terminology. If you talk about a list of "consecutive" odd integers, say, then the second thing in the list follows the first thing, in sequence - the second term must be larger than the first term. But here they intend the sequence of ...”
May 14, 2019
Ian Stewart posted a reply to In the xy-coordinate system, rectangle ABCD is inscribed in the Problem Solving forum
“If a circle has the equation x^2 + y^2 = r^2, then it is a circle centered at the origin, with radius r. So our circle here is a circle of radius 5, centered at (0, 0). So, if a diagonal of the inscribed rectangle lies on the x-axis, the coordinates of its endpoints must be (-5, 0) and (5, 0). We ...”
May 14, 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
GMATGuruNY posted a reply to A retail store employs only clerks and managers and the in the Problem Solving forum
“Last year''s payroll = (number of employees)(average hourly wage) = 20*13 = 260. This year 4 clerks are hired, increasing the number of employees to 24. Since the average hourly wage this year = 14, we get: This year''s payroll = (number of employees)(average hourly wage) = 24*14 = 336. ...”
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
Ian Stewart posted a reply to 50 students of a certain class took a test. How many of them in the Data Sufficiency forum
“Using both Statements, it''s possible all 50 students got a score of ''82'', or it''s possible that 25 of them got ''81'' and 25 of them got ''83'', among other possibilities. So the answer is E.”
May 13, 2019
Ian Stewart posted a reply to A jar contains exactly 100 marbles; each marble contains in the Data Sufficiency forum
“If we have 100 marbles, and each marble is made up of 2 colours, we have 200 colours in total. Using either Statement alone, we haven''t accounted for very many of the colours, so we could have quite a few half-blue marbles or we could have none, and our probability of picking half-blue marbles ...”
May 13, 2019
Ian Stewart posted a reply to Cotto Toy Store sells Product X and Product Y at two in the Data Sufficiency forum
“Neither Statement is sufficient alone, because if the initial price of X is enormously larger than the initial price of Y, using either Statement alone, the discounted price of X will remain larger, and similarly if the initial price of Y is vastly larger than that of X, so will be Y''s discounted ...”
May 13, 2019
Ian Stewart posted a reply to Maria can either buy a basket that contains P pounds of in the Data Sufficiency forum
“The basket costs $16.50, and the p pounds of apples cost $0.95p. We want to know which of those figures is larger. Statement 1 is irrelevant, since we don''t care how many apples are in the basket -- we already know the basket costs $16.50. What we need is information about the p pounds of ...”
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
Ian Stewart posted a reply to What percent of the children in the class are holding a in the Data Sufficiency forum
“The answer is instantly C or E, since we''ll need to know about both boys and girls. Using both statements, we have a standard weighted average situation. If k% of boys and m% of girls are holding a popsicle, then somewhere between k% and m% of the group as a whole is holding a popsicle, where the ...”
May 13, 2019
Ian Stewart posted a reply to S is a set of points in the plane. How many distinct in the Data Sufficiency forum
“We clearly need to know how many points we have, since if we have, say, only 2 points, we can''t draw any triangles, but if we have many points that aren''t all in a line, we can draw at least one triangle. So Statement 1 is indispensable. But knowing we have exactly 5 points is not sufficient, ...”
May 13, 2019
Ian Stewart posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum
“In general, if you know all three angles in a triangle (which we do here, since from two angles we can find the third using the fact that a triangle''s angles sum to 180), and you know one of the triangle''s sides, the other two sides are completely determined, so it must somehow be possible to work ...”
May 13, 2019
Ian Stewart posted a reply to Automobile A is traveling at two-thirds the speed that Autom in the Data Sufficiency forum
“Each Statement gives the same type of relationship between the two speeds, so the answer will be C, D or E. If we let a and b be the two speeds of the cars, we know that a = 2b/3. Using Statement 1 alone, you might be able to see by inspection that the speeds are 20 and 30. Or we can use ...”
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
GMATGuruNY posted a reply to According to public health officials in the Sentence Correction forum
“Incorrect: More babies were born in 1900 than they were born in 1800. Here, the usage of they implies that the SAME BABIES born in 1900 were also born in 1800 -- a nonsensical meaning. Generally: When a comparison begins with MORE/FEWER + SUBJECT + VERB, the implied clause after than should NOT ...”
May 13, 2019
GMATGuruNY posted a reply to An auto dealer sells each car at either $20,000 or $30,000. in the Data Sufficiency forum
“Statements combined: Case 1: 30 $30,000 cars are marked up 30%'' 20 $20,000 cars are marked up 20% Case 2: 10 $30,000 cars are marked up 30% 20 $20,000 cars are marked up 30% 20 $30,000 cars are marked up 20% In Case 1, the more expensive $30,000 cars are all sold at the higher profit ...”
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
GMATGuruNY posted a reply to OG 13 #9 in the Sentence Correction forum
“When a statistic decreases in value, we use lower rather than less. Incorrect: The temperature was less in the second experiment than in the first. Correct: The temperature was lower in the second experiment than in the first. Most of the country’s biggest daily newspapers had lower ...”
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
GMATGuruNY posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum
“Alternate approach: There are 6 slots in the season: 3 wins, 2 losses and 1 draw. From the 6 slots, the number of ways to choose 3 to be occupied by the 3 wins = 6C3 = (6*5*4)/(3*2*1) = 20. From the 3 remaining slots, the number of ways to choose 2 to be occupied by the 2 losses = 3C2 = ...”
May 11, 2019
GMATGuruNY posted a reply to OG 13 #9 in the Sentence Correction forum
“Here, greater serves to modify not costs but PROPORTION. Conveyed meaning: The PROPORTION in the presidential campaign of 1992 was greater than the PROPORTION in any previous election. When comparing elements with regard to WEIGHT, we generally use not lower but LESS. Adam weighs LESS than ...”
May 11, 2019
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1 In this case, (a-b)/6 = C.”
May 11, 2019
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1 In this case, (a-b)/6 = C.”
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
GMATGuruNY posted a reply to According to surveys by the National Institute on Drug Abuse in the Sentence Correction forum
“Proposed revision: as many young adults as the 1997 survey reported Conveyed meaning: The 1997 survey reported many young adults. This meaning seems illogical. The 1997 survey reported a NUMBER. It did not report the young adults themselves.”
May 10, 2019
GMATGuruNY posted a reply to Ellipsis question in the Sentence Correction forum
“OA: Today, the same amount of acreage produces twice as many apples as it did in 1910. The phrase in blue conveys that the amount of acreage producing apples today is the SAME as the amount that produced apples in 1910. For example: If 100 acres produced apples in 1910, then 100 acres are ...”
May 10, 2019
GMATGuruNY posted a reply to An art gallery has only paintings and sculptures. Currently, in the Problem Solving forum
“This is an EITHER/OR group problem. Every piece of art is EITHER a painting OR a sculpture. Every piece of art is EITHER displayed OR not displayed. For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data. Let P = paintings, S = ...”
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
Ian Stewart posted a reply to In an integer division operation, the divisor is x, the quot in the Data Sufficiency forum
“You don''t need to know what a "dividend" is on the GMAT, and if this were a real GMAT question it would declare that all of the numbers are positive. In this question, we''re dividing z by x, and getting a quotient of y and a remainder of r. So z = xy + r Using either Statement ...”
May 8, 2019
GMATGuruNY posted a reply to The sum of two numbers is 1 and their product is -1. What is in the Problem Solving forum
“x³ + y³ = (x+y)(x²+y²-xy) Since x+y=1, we get: (x+y)² = 1² x² + y² + 2xy = 1 Substituting xy=-1 into x² + y² + 2xy = 1, we get: x² + y² + 2(-1) = 1 x² + y² = 3 Substituting x+y=1, x²+y²=3 and xy=-1 into x³ + y³ = (x+y)(x²+y²-xy), we get: x³ + y³ = (1)(3-(-1)) = ...”
May 8, 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
GMATGuruNY posted a reply to According to surveys by the National Institute on Drug Abuse in the Sentence Correction forum
“Correct! The OA to SC71 in the OG11 includes a similar construction: The cameras of the Voyager II spacecraft detected six small, previously unseen moons circling Uranus, doubling...the number of satellites now known to orbit the distant planet.”
May 7, 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
GMATGuruNY posted a reply to GMATPrep SC in the Sentence Correction forum
“Here, much and the increase are redundant, since both words refer to an amount. Proposed revision: The number of people flying first class on domestic flights rose sharply in 1990, twice the increase of the previous year. Implied comparison: The NUMBER OF PEOPLE flying in 1990 was twice ...”
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
Ian Stewart posted a reply to For any sequence of \(n\) consecutive positive integers, in the Problem Solving forum
“If you take the sequence 1, 2, the sum of the even integers is 2 and the sum of the odd integers is 1, so \(S_e > S_o\) and item 1 can be true. If you take the sequence 2, 3, the sum of the even integers is 2 and the sum of the odd integers is 3, so \(S_e < S_o\), and item 3 can be true. ...”
May 7, 2019
Ian Stewart posted a reply to \(A\) and \(B\) are the endpoints of the longest line that in the Problem Solving forum
“The longest line you can draw in a circle is a diameter, so AB is a diameter of the circle. If X is the center of the circle, then AX is a radius. The question tells us AX is 3, so the radius of the circle is 3. If you draw a diagram, and look at triangle ACX, two of the sides of that triangle, ...”
May 7, 2019
Ian Stewart posted a reply to If \(x\) is a positive integer, is \(x\) a prime integer? in the Data Sufficiency forum
“Statement 1 tells us x is one less than some prime number. If that prime is 3, then x=2, and x is prime, but if that prime is 5, x=4, and x is not prime, so Statement 1 is not sufficient. Statement 2 tells us x is 5 greater than some prime number. If that prime is 2, then x=7, and x is prime, but ...”
May 7, 2019
Ian Stewart posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum
“4^b is always positive, no matter what b is. If a^3 = -27, then a is negative and so is a^5. So it''s certainly true that a^5 < 4^b, because negative numbers are smaller than positive numbers. So Statement 1 is sufficient. Statement 2 is not sufficient; while we know b is either 4 or -4, we ...”
May 7, 2019
GMATGuruNY posted a reply to If each child in a group of children received either one or in the Data Sufficiency forum
“Let x = the number of children receiving 2 candies each and y = the number of children receiving 1 candy each. Thus: Total number of candies = 2x + y. Question stem, rephrased: What is the value of x? Statement 1: Of every 4 children, 1 receives 2 candies and 3 each receive 1 candy. ...”
May 7, 2019
GMATGuruNY posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum
“A 3-person committee that includes Michael will be composed of Michael and two other people chosen from the remaining five members. From 5 members, the number of ways to choose 2 = 5C2 = 10. Of these 10 pairs, the number that will include Anthony = 4. (Since there are 4 other people who could ...”
May 7, 2019
GMATGuruNY posted a reply to A bucket full worns in the Problem Solving forum
“Let the number of worms = 60. Since the rat eats 1/6 of the 60 worms -- in other words, 10 worms -- in 5 hours, the rat''s rate = w/t = 10/5 = 2 worms per hour. 1/4 of the 60 worms = 60/4 = 15 worms. Since the rat''s rate = 2 worms per hour, the time for the rat to eat 15 worms = w/r = 15/2 = 7.5 ...”
May 7, 2019
GMATGuruNY posted a reply to A book has 1000 pages numbered 1, 2, 3, …, and so on. How in the Problem Solving forum
“Ignore page 1000, since it does not include the digit 2. To make the calculation easier, consider the remaining pages numbered as 3-digit integers, beginning with 000 and ending with 999: 000, 001, 002...997, 998, 999 There are 1000 options between 000 to 999, inclusive. Since each option is ...”
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
Ian Stewart posted a reply to A six-sided mosaic contains 24 triangular pieces of tile in the Data Sufficiency forum
“If we know each triangle is equilateral with sides of length 9, and we know how many triangles we have, of course we can find the area of all of them, so Statement 1 is sufficient. That we can fit the mosaic in some rectangle limits how large the mosaic might be, but we have no idea how much ...”
May 6, 2019
GMATGuruNY posted a reply to The equation (M + 6)/36 = (p – 7)/21 relates two temperatu in the Problem Solving forum
“If M=30 and P=28, both sides of (M + 6)/36 = (P – 7)/21 are equal to 1. The correct answer must yield a valid equation for M=30 and P=28. When the question stem includes the phrase "which of the following," the correct answer is likely to be D or E. E: M = (12/7)P – 18 If M=30 ...”
May 6, 2019
GMATGuruNY posted a reply to What is the remainder when the product of the first 10 prime in the Problem Solving forum
“What is the remainder when 30 is divided by 4? One approach: 1. Break the dividend 30 into factors: 30 = 5*6 2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2 3. Multiple the resulting remainders: 1*2 = 2 Step 3 indicates that 30 divided by 4 will yield a remainder of 2. ...”
May 6, 2019
Ian Stewart posted a reply to Mr. Wayne bungee jumps from the top of a building straight in the Problem Solving forum
“In 15-3 = 12 seconds, he passes 20 - 5 = 15 floors. If each floor is 3 meters, he covers a distance of 45 meters. So his speed is 45/12 = 15/4 = 3.75 m/s. Of course if each floor is 3 meters high, it''s not clear what it means to ''pass a floor'' (when during the 3 meters do we consider the ...”
May 5, 2019
Ian Stewart posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum
“If we have a two digit number AB, where A is the tens digit and B the units digit, then the number is equal to 10A + B. So here, if A and B represent digits, our numbers are AB and BA. These are equal to 10A + B and 10B + A, and their sum is equal to 11A + 11B. This sum is clearly divisible by ...”
May 5, 2019
Ian Stewart posted a reply to In 1994, Company X recorded profits that were 10% greater in the Data Sufficiency forum
“We already know the ratio of the company''s profits in 1994 to profits in 1992, since we''re told the percent changes from year to year in the stem, so Statement 2 just restates information we already know, and is useless. If in 1994 the company profits were $100,000 greater than in 1993, and ...”
May 5, 2019
GMATGuruNY posted a reply to If a jury of 12 people is to be selected randomly from a in the Problem Solving forum
“Question rephrased: What is the probability that at least 8 men will be selected to serve on the 12-member jury? P(good outcome) = 1 - P(bad outcome). Here, a BAD outcome means selecting a jury with FEWER than 8 men. Of the 10 men and 5 women in the jury pool, 3 people must be selected NOT ...”
May 5, 2019
Ian Stewart posted a reply to The 9 squares above are to be filled with x's and o's in the Data Sufficiency forum
“From Statement 1, we know we have at least 5 O''s, and therefore at most 4 X''s. From Statement 2, we know we have at least 4 X''s, in the four corners. Neither statement is sufficient, but using both, if we have at least 4 X''s and at most 4 X''s, we must have exactly 4 X''s, and the two ...”
May 5, 2019
Ian Stewart posted a reply to In the figure above, triangle PQR has angle measures as in the Data Sufficiency forum
“If PQ = QR, the triangle is isosceles, and we have two equal angles opposite PQ and QR. So we have two 58 degree angles (x = 58), and since the sum of the three angles in a triangle is 180, we can find the third angle y and answer the question. In a triangle, the longest side is opposite the ...”
May 5, 2019
Ian Stewart posted a reply to When Tom works alone he chops 2 lbs salad in 3 minutes, and in the Problem Solving forum
“Getting the same time, 6 minutes, for both: Tom chops 4 lbs in 6 minutes Tammy chops 9 lbs in 6 minutes So when they work for the same amount of time, the ratio of the amount Tammy chops to the amount Tom chops is 9 to 4, and since 9 is 125% greater than 4, the answer is 125%. The 65 lbs in ...”
May 4, 2019
Ian Stewart posted a reply to What is the sum of all values of that satisfy the equation in the Problem Solving forum
“We can divide by 4 and get zero on both sides: 4x^2 + 16 = 32x x^2 + 4 = 8x x^2 - 8x + 4 = 0 When we factor the left side above, the factorization will look like (x - a)(x - b), where a and b are the two solutions to the quadratic. The numbers a and b will multiply to 4 (since 4 = (-a)(-b) = ...”
May 4, 2019
Ian Stewart posted a reply to Teachers in United States high schools teach an average in the Problem Solving forum
“Standard deviation is the square root of variance (a fact you almost certainly will not need to know on the GMAT), so the standard deviation here is 10, two standard deviations is thus 20, and 60 and 100 are the two values that are two standard deviations away from the mean of 80. Only 60 is an ...”
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
“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
Ian Stewart posted a reply to If x represents the number of positive factors of integer y in the Data Sufficiency forum
“A number has an odd number of divisors only if that number is a perfect square. It''s easy to see why: for a number that is not a perfect square, say 6, then all of the divisors can be ''paired up'' into pairs that produce 6 as a product: 1 and 6 2 and 3 so we have an even number of divisors. ...”
May 4, 2019
Ian Stewart posted a reply to If the positive integer \(x\) is rounded to the nearest ten, in the Data Sufficiency forum
“The question is just asking "is the units digit of x greater than 5?" When we divide a positive number by 10, the remainder we get is that number''s units digit, so Statement 1 tells us "the units digit of x is even". It could be 0, 2, 4, 6 or 8, so we can''t answer the ...”
May 4, 2019
GMATGuruNY posted a reply to 7, 9, 6, 4, 5, x If x is a number in the list above in the Data Sufficiency forum
“Given numbers in ascending order: 4, 5, 6, 7, 9 Statement 1: Smallest 3 numbers are 4, 5, and 6. Greatest 3 numbers are 7, 9 and x, where x is any number greater than 7. Thus: Median = average of the 2 middle numbers =(6+7)/2 = 6.5. SUFFICIENT. Rule: For any set that is SYMMETRICAL ...”
May 4, 2019
GMATGuruNY posted a reply to Romeo and Juliet play a dice game in which the two in the Problem Solving forum
“Let P(R) = the probability that Romeo wins and P(J) = the probability that Juliet wins. Since there are only two possible outcomes -- either Romeo wins or Juliet wins -- we get: P(R) + P(J) = 1 Probability that Romeo wins on the first roll = 1/6 Probability that Romeo wins on the third roll ...”
May 3, 2019
Ian Stewart posted a reply to Operation F means “take the square root,” operation G me in the Problem Solving forum
“If we multiply our positive number x by a negative constant c, then take the square root, we get something undefined. And if we multiply x by 0, then take a reciprocal, we get something undefined. So if we''re supposed to be able to apply these functions in any order, just to get something that ...”
May 3, 2019
Ian Stewart posted a reply to In the \(xy-\)plane above, is angle \(BAC\) greater than in the Data Sufficiency forum
“They should be clear in Statement 2 what angles they''re describing - around a point, there are two different angles you can make, the small angle within the triangle, and the large angle around the outside of the triangle (the one that would sum to 360 with the angle inside the triangle). But as ...”
May 3, 2019
Ian Stewart posted a reply to At a restaurant, five friends each purchased a sandwich. in the Data Sufficiency forum
“Presumably they mean to ask about the sum of the prices of the sandwiches, and not about the sum of the sandwiches themselves. If Statement 1 is true, all we can say is that the sum of the prices exceeded 5*13 = $65, so that''s not sufficient. If Statement 2 is true, all we can say is that the ...”
May 3, 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
GMATGuruNY posted a reply to Tickets for all but 100 seats in a 10,000-seat stadium were in the Problem Solving forum
“If all 10,000 tickets are sold, we get: 20% sold for $1 each = 2000*1 = 2,000 80% sold for $2 each = 8000*2 = 16,000 Total revenue = 2000+16000 = 18,000 Since 100 tickets are not actually sold, the total revenue must be a bit less than 18,000. The correct answer is B.”
May 2, 2019
GMATGuruNY posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we ...”
May 2, 2019
GMATGuruNY posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we ...”
May 2, 2019
Ian Stewart posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can work out the probability he continues to get unmatched socks, and once that probability falls below 1/2, we''ll know he has a greater than 1/2 chance of getting at least one pair of matched socks. The first sock he picks doesn''t matter. The next sock has a 10/11 chance of not matching the ...”
May 2, 2019
Ian Stewart posted a reply to After the first two terms in a sequence of numbers, each in the Data Sufficiency forum
“If the sum of the first 3 terms is 6, then according to the definition of the sequence, the 4th term is 6. But then the fifth term is just the sum of the first 3 terms plus the 4th term, so is 6+6 = 12. Statement 1 is sufficient. If the 4th term is 6, then by the definition of the sequence, the ...”
May 2, 2019
Ian Stewart posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum
“If Jones has worked twice as many years as Green, and has also worked 5 years longer than Green, then Green has worked 5 years and Jones has worked 10. So Statement 2 is sufficient. We can deduce from Statement 1 that Jones has worked 5 years longer than Green, so Statement 1 is also sufficient, and ...”
May 2, 2019
GMATGuruNY posted a reply to Train A leaves the station at 5:00, and travels north at 50 in the Data Sufficiency forum
“Statement 1: From 5pm to 6pm, A travels on its own for 1 hour at a rate of 50 mph, with the result that A travels ahead 50 miles. Since B''s rate is unknown, we cannot determine when B catches up to A. INSUFFICIENT. Statement 2: Since A''s 50-mph rate is 5/6 of B''s rate, we get: 50 = ...”
May 1, 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
Ian Stewart posted a reply to At a community center, three separate pumps- A, B, and C in the Data Sufficiency forum
“If C alone fills 3/10 of the pool in 126 minutes, it fills the whole pool in (10/3)(126) = 1260/3 = 420 minutes, or 7 hours. So C alone would fill the pool at 3pm, even with no help from A or B, and Statement 1 is sufficient. If A+B together fill 1/8 of the pool in 55 minutes, they fill the whole ...”
May 1, 2019
Ian Stewart posted a reply to The total price of 5 pounds of regular coffee in the Data Sufficiency forum
“Since we''re never given any information about price per pound, the numbers in "5 pounds" and "3 pounds" are just a distraction. All we''re doing here is mixing some regular coffee and some decaf coffee. Say all the regular coffee costs $R and all the decaf costs $D. The stem ...”
May 1, 2019
GMATGuruNY posted a reply to x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2? in the Problem Solving forum
“x² + 4x + 1 = 0 Dividing both sides by x, we get: (x² + 4x + 1)/x = 0/x x + 4 + 1/x = 0 x + 1/x = -4 Squaring both sides, we get: (x + 1/x)² = (-4)² x² + 1/x² + 2(x)(1/x) = 16 x² + 1/x² + 2 = 16 x² + 1/x² = 14 The correct answer is C.”
May 1, 2019
Ian Stewart posted a reply to Is the average (arithmetic mean) of 5 different positive in the Data Sufficiency forum
“If the five numbers are, as Statement 1 and the stem tell us, five different positive multiples of 10, the smallest values we could possibly have are: 10, 20, 30, 40, 50 That''s an equally spaced list, so its average is equal to its median, so the average of the list above is 30. But that''s ...”
May 1, 2019
Ian Stewart posted a reply to A certain painting job requires a mixture of yellow, green, in the Data Sufficiency forum
“From Statement 1, 1/4 of the mixture is green paint, and since we know we have 12 quarts of paint in total, we must have 3 quarts of green paint. So Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about what fraction of the mixture is white paint.”
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
GMATGuruNY posted a reply to For all his professed disdain of such activities, Auden was in the Sentence Correction forum
“When a sentence begins with for all + POSSESSIVE, for all = DESPITE. OA: For all his professed disdain of such activities, Auden was an inveterate literary gossip. Conveyed meaning: Despite his professed disdain of such activities, Auden was an inveterate literary gossip. E: In spite of ...”
April 30, 2019
GMATGuruNY posted a reply to Is x+y>0? in the Data Sufficiency forum
“Statement 1: Here, x and y must have the SAME SIGN. If x and y are both positive, then x+y > 0. If x and y are both negative, then x+y < 0. INSUFFICIENT. Statement 2: The inequality implies that x and y are both NONZERO. Since the square of a nonzero value must be positive, we can ...”
April 30, 2019
GMATGuruNY posted a reply to Last year, the average price of eight different products in the Data Sufficiency forum
“We can determine this year''s average price if we know the difference between this year''s revenue and last year''s. Statements combined: Case 1: Last year the 5 products in Statement 1 had an average price of $10, for a total of $50 in revenue In this case, the increase in revenue yielded by ...”
April 30, 2019
Ian Stewart posted a reply to If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times 4^7, what in the Problem Solving forum
“Just factor out 4^7 from the sum in the numerator: (4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7 4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7 and now if we divide by 4^7 on both sides, we have 1 + 4 + 4^2 + 4^3 = 5x 85 = 5x 17 = x”
April 30, 2019
Ian Stewart posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“We can just check each of the four arithmetic operations to see when each Statement will be true. If r = s, we can replace ''s'' with ''r'', so for Statement 1: r+r = 2r r-r = 0 r*r = r^2 r/r = 1 and it''s only when the operation is subtraction that we get 0 as a result, and the operation ...”
April 30, 2019
Ian Stewart posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Statement 1 tells us that n is equal to 13, so of course we can answer any question about n, and Statement 1 is sufficient. The remainder you get when you divide by 4 has no relationship to the remainder you get when you divide by 5, so Statement 2 is useless. For example, n could be 5, and then ...”
April 30, 2019
Ian Stewart posted a reply to In a certain first grade classroom, the average height is in the Data Sufficiency forum
“The sum of the 5 girls'' heights is 5x, and the sum of the 8 boys'' heights is 8y, so the average height is (5x + 8y)/13. So if we can find the value of 5x + 8y, we can answer the question. From Statement 1, dividing by 3 on both sides, we find 15x + 24y = 1755 5x + 8y = 1755/3 so we can ...”
April 30, 2019
Ian Stewart posted a reply to Last year, the average price of eight different products in the Data Sufficiency forum
“The answer is instantly C or E, because using either statement alone, we don''t know anything about some of the products. Using both Statements, it''s possible, say, that five of the products cost $0.10 each, and the other three cost more than $600 each. If the five cheap products increased in ...”
April 30, 2019
Ian Stewart posted a reply to A drawer contains 12 socks, of which 8 are black and 4 are in the Data Sufficiency forum
“We have 9 socks left. If, as Statement 1 tells us, the ratio of black to white socks is 2 to 1, then 2/3 of the remaining socks are black, and thus 6 are black, so Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about the third sock that was removed, so the ...”
April 30, 2019
GMATGuruNY posted a reply to A basketball coach has won 65 percent of the 400 games she in the Problem Solving forum
“Total games = (400 games already played) + (100 additional games) = 500. Required number of wins = 70% of 500 = 350. Current number of wins = 65% of 400 = 260. Additional wins needed = 350-260 = 90. The correct answer is D.”
April 30, 2019
GMATGuruNY posted a reply to What is the remainder when 1044*1047*1050*1053 is in the Problem Solving forum
“What is the remainder when 30 is divided by 4? One approach: 1. Break the dividend 30 into factors: 30 = 5*6 2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2 3. Multiple the resulting remainders: 1*2 = 2 Step 3 indicates that 30 divided by 4 will yield a remainder of 2. ...”
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
Ian Stewart posted a reply to If a and b are integers and a is even, what is the value in the Data Sufficiency forum
“Using both Statements, we might have a=2 and b=7, or we might have a = -2000 and b = -7000, among other possibilities, and we can easily get different values for a-b, so the answer is E.”
April 29, 2019
Ian Stewart posted a reply to The inflation index for the year 1989 relative to the year in the Data Sufficiency forum
“We know that the ratio of the price of the mixer in 1989 to the price in 1970 was 3.56 to 1. Notice then that for every dollar the mixer cost in 1970, the price increased by $2.56. So if the actual increase was $102.40, the cost in 1970 must have been 102.40/2.56, and Statement 1 is sufficient. ...”
April 29, 2019
Ian Stewart posted a reply to K is a set of integers such that if the integer r is in K in the Data Sufficiency forum
“If we know r is in K, then we know r+1 is in K. So if 50 is in K, we know that 51 is in K, but then we know 52 is in K, and 53 is in K, and so on, so 100 will be in K. So Statement 1 is sufficient. From Statement 2, we know 150 is in K, so we know 151, 152, 153 etc are also in K. But we don''t ...”
April 29, 2019
Ian Stewart posted a reply to A total of 20 amounts are entered on a spreadsheet that has in the Data Sufficiency forum
“If you have 4 values, and R is their average, then 4R is their sum, from the definition of an average (just rewrite average = sum/n so you have ''sum'' on one side). So here, 4R(1) is the sum of the four values in row 1, 4R(2) is the sum of the four values in row two, and so on, and thus 4[ R(1) ...”
April 29, 2019
Ian Stewart posted a reply to If m is an integer, is m/102 an integer? in the Data Sufficiency forum
“Prime factorize: 102 = 2*51 = 2*3*17 So we can be certain m/102 is an integer if we can be certain m is divisible by 2, 3 and 17. Statement 1 tells us 165m is divisible by 99, or that 165m/99 is an integer. So (33)(5m)/(33)(3) is an integer, and 5m/3 is an integer. That means the ''3'' in the ...”
April 29, 2019
Ian Stewart posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum
“We can rewrite the question: Is (a-1)/(b+1) = a/b ? Is ab - b = ab + a ? Is -b = a? from which we can see that Statement 2 tells us exactly what we want, while Statement 1 does not (if Statement 1 is true, the answer may be ''yes'', if b = 2 and a = -2, but can also be no for any other ...”
April 29, 2019
Ian Stewart posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum
“The average of an equally spaced set is equal to the median of that set, so here, if p, r, s are consecutive integers in increasing order, their average is simply r, so r = x and the question is just asking if we can find r. Notice also that the sum of the three integers is therefore 3r (because by ...”
April 29, 2019
Ian Stewart posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum
“If you expand the left side of Statement 1, we have (x + m)(x + n) = x^2 + 5x + mn x^2 + (m+n)x + mn = x^2 + 5x + mn and now most of the terms can be subtracted from both sides, leaving us with (m + n)x = 5x and dividing by the nonzero x, we find m+n = 5, so Statement 1 is sufficient. ...”
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
GMATGuruNY posted a reply to What is the units digit of the number z? in the Data Sufficiency forum
“Statements combined: Case 1: z=19, with the result that z is between both 17 and 20 and 18 and 21 In this case, the units digit of z is 9. Case 2: z=18.1, with the result that z is between both 17 and 20 and 18 and 21 In this case, the units digit of z is 8. Since the units digit can be ...”
April 28, 2019
GMATGuruNY posted a reply to The number line shown contains three points R, S, and T in the Problem Solving forum
“Let R=-3, S=3 and T=6, implying that r=|-3|=3, s=|3|=3, and t=|6|=6. Average of R, S, and T = (-3+3+6)/3 = 2. The correct answer must yield 2 when r=3, s=3 and t=6. Only E works: (s + t - r)/3 = (3+6-3)/3 = 6/3 = 2 The correct answer is E.”
April 28, 2019
GMATGuruNY posted a reply to Peter and Tom shared the driving on a certain trip. in the Problem Solving forum
“Let the total distance = 5 miles and the time for each driver = 1 hour. Since Peter drives 2/5 of the total distance -- 2 miles -- in 1 hour, Peter''s speed = d/t = 2/1 = 2 miles per hour. Since Tom drives the remaining distance -- 3 miles -- in 1 hour, Tom''s speed = d/t = 3/1 = 3 miles per ...”
April 28, 2019
Ian Stewart posted a reply to S is a set of integers such that i) if a is in S, then in the Data Sufficiency forum
“Using Statement 1 alone, if ''1'' is in the set, then from rule i), we can deduce that -1 is in the set. But then using rule ii), we can''t generate any new values besides 1 and -1. So there are only two values, 1 and -1, that we can be certain are in the set, and we have no way to know if -4 is in ...”
April 28, 2019
Ian Stewart posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum
“Statement 1 isn''t sufficient, since it just tells us one other value in the set. Statement 2 also isn''t sufficient alone -- while using it we can determine many other values in the set (all the positive and negative powers of 3 are in the set), we have no way to know if -15 is in the set, since ...”
April 28, 2019
Ian Stewart posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum
“Statement 1 tells us exactly what kind of integers we have, so using the familiar even/odd rules, we can work out if the sum will be even or odd (since odd+odd is even, and even+even is even, the sum will turn out to be even, though since it''s a DS question, we don''t actually care what the answer ...”
April 28, 2019
Ian Stewart posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum
“Statement 1 tells us that the fifth term is either 0 or 2. There''s no other information anywhere in the question that tells us anything about the fifth term in the sequence, so using both statements, we have two possibilities, and the answer is E.”
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
GMATGuruNY posted a reply to Ten theater students are to begin work on a set for a musica in the Problem Solving forum
“(50 days)/(60 days) = 5/6. To finish the job in 5/6 of the normal time, the crew requires 6/5 of the normal number of students -- an increase of 1/5: (1/5)(10) = 2 more students. The correct answer is A.”
April 27, 2019
Ian Stewart posted a reply to If \(n\) and \(m\) are positive integers, what is the in the Data Sufficiency forum
“If you divide a number by 10, the remainder you get is just the number''s units digit. So the question is just asking "what is the units digit of \(3^{(4n+2)}+m\) ?" There are other units digit/exponent methods that are more flexible, but I''ve explained those in other posts, so I''ll ...”
April 26, 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
GMATGuruNY posted a reply to OG Most of the country's biggest daily newspapers in the Sentence Correction forum
“Plural terms such as profits, revenues, costs, etc. refer to NUMERICAL VALUES. When comparing plural terms that refer to numerical values, we generally do not use more but instead use -ER comparatives such as higher, lower, greater, etc. Thus, the blue sentence above is correct; the red sentence ...”
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
GMATGuruNY posted a reply to Suppose x = a/b (b≠0). Which of following is equivalent to in the Problem Solving forum
“Let a=2 and b=1, with the result that x = a/b = 2/1 = 2 and that (a²+ab)/(a²+b²) = (4+2)/(4+1) = 6/5. The correct answer must yield 6/5 when x=2. Only A works: (x²+x)/(x²+1) = (4+2)/(4+1) = 6/5 The correct answer is A.”
April 25, 2019
GMATGuruNY posted a reply to Probability Question in the Problem Solving forum
“The approach above counts the following: Cases that include 11: 1122, 1133, 1144, 1155, 1166 Cases that include 22: 2211, 2233, 2244, 2255, 2266 Cases that include 33: 3311, 3322, 3344, 3355, 3366 Cases that include 44: 4411, 4422, 4433, 4455, 4466 Cases that include 55: 5511, 5522, ...”
April 25, 2019
GMATGuruNY posted a reply to On account of a law in the Sentence Correction forum
“The OA is correct because it contains no grammatical errors and conveys a logical meaning. OA: With the cost of wireless service plummeting, many people are now using their mobile phones. Here, the action in blue is accompanied by the plummeting cost of wireless service. This meaning is perfectly ...”
April 24, 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
Ian Stewart posted a reply to If the positive integer x divisible by 200? in the Data Sufficiency forum
“If we prime factorize everything: The question asks if x is divisible by 2^3 * 5^2 From S1: x^2 is divisible by 2^3 * 5^4. For x^2 to be divisible by 2^3, it will need to be true that x itself is divisible by at least 2^2, since if x were only divisible by 2^1, then x^2 would only be divisible ...”
April 23, 2019
Ian Stewart posted a reply to A number when divided successively by 4 and 5 leaves in the Problem Solving forum
“The question means something different from what it actually says, but I can guess what it''s trying to say. When we take our number, "n", and divide it by 4, we get a remainder of 1. So n is exactly 1 greater than some multiple of 4, and we have: n = 4q + 1 It''s here where the ...”
April 22, 2019
Ian Stewart posted a reply to What is the area of the shaded region in the figure shown? in the Data Sufficiency forum
“Draw a vertical line starting from point E, up to the line BC. That line will divide the large rectangle (ABCD) into two smaller rectangles. Line BE cuts one of those smaller rectangles in half along the diagonal, while line EC cuts the other one in half along the diagonal. So half of each smaller ...”
April 22, 2019
Ian Stewart posted a reply to What is the value of x? in the Data Sufficiency forum
“From Statement 1, x must be 5. From Statement 2, either x-3 = 2, or x-3 = -2, which gives us two different values for x (5 and 1). So the answer is A.”
April 22, 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
Ian Stewart posted a reply to At a community event, the total number of men, women, and in the Data Sufficiency forum
“If the ratio of men to women to children is 15 to 32 to 17, then (since that ratio is reduced) the total number of people must be a multiple of 15+32+17 = 64. If the total is also less than 120, it can only be exactly 64, so we have exactly 15 men, and Statement 1 is sufficient. Statement 2 is ...”
April 22, 2019
GMATGuruNY posted a reply to Probability Question in the Problem Solving forum
“All possible rolls: Since there are 6 number options for each roll, we get: 6*6*6*6 = 1296 Case 1: Exactly 2 rolls are the same (such as 1123) From 4 rolls, the number of ways to choose a pair to yield the same number = 4C2 = (4*3)/(2*1) = 6. Number options for this pair = 6. (Any of the 6 ...”
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
GMATGuruNY posted a reply to If j > 1, is integer j a prime number? in the Data Sufficiency forum
“Statements combined: Since dividing by 3 or 2 leaves a remainder of 1, j must be 1 more than a multiple of 3 and 2: j = (3*2)a + 1 = 6a + 1, where a is a positive integer Options for j: 7, 13, 19, 25... If j=7, then the answer to the question stem is YES. If j=25, then the answer to the ...”
April 21, 2019
GMATGuruNY posted a reply to From a group of 5 managers (Joon, Kendra, Lee, Marnie and in the Problem Solving forum
“Approach 1; P = (good pair)/(all possible pairs) Good pair = Marnie and Noomi = 1 option. All possible pairs = the number of ways to select 2 managers from 5 options = 5C2 = (5*4)/(2*1) = 10 options. Thus: P = 1/10 = 0.1 Approach 2: P(M or N is selected first) = 2/5. (Of the 5 managers, 2 ...”
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
GMATGuruNY posted a reply to While it costs about the same in the Sentence Correction forum
“Here, the phrase in blue implies that people were trying to drive on the freeway but that the process was made challenging by the rain. This meaning is logical. Here, the phrase in red implies that nuclear plants are trying to generate electricity but that the process is made more expensive ...”
April 20, 2019
GMATGuruNY posted a reply to Discussion of greenhouse effects has usually in the Sentence Correction forum
“An effect is a CHANGE brought about by an event. The Earth ALWAYS has a temperature. Since temperature does not constitute a change, it cannot be an effect. In the OA, EXTREMES are the change brought about by greenhouse emissions. This meaning is logical. The temperature of the Earth is not ...”
April 20, 2019
GMATGuruNY posted a reply to What is the value of |x|? in the Data Sufficiency forum
“Statement 1: Case 1: x=0, with the result that -|x| = - |0| = 0 In this case, |x| = 0. Case 2: x=-1, with the result that -|-1| = -1 In this case, |x| = 1. Since |x| can be different values, INSUFFICIENT. Statement 2: Thus, x=2 or x=-2. In each case, |x|=2. SUFFICIENT. The correct ...”
April 20, 2019
GMATGuruNY posted a reply to Mary's income is 60 percent more than Tim's income, and in the Problem Solving forum
“Let J=100. Since Tim''s income is 40% less than Juan''s, T = 100 - (40% of 100) = 100 - 40 = 60. Since Mary''s income is 60% greater than Tim''s, M = 60 + (60% of 60) = 60 + 36 = 96. What percent of Juan''s income is Mary''s income? M/J = 96/100 = 96%. The correct answer is C.”
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
Ian Stewart posted a reply to A certain money market account that had a balance of $48,000 in the Problem Solving forum
“If it earns $360 in a month, it earns $360 *12 in a year, if there''s no compounding. Dividing by the amount invested, we''ll get the interest rate for the year: (12)(360)/48000 = 1*360/4000 = 36/400 = 9/100 = 9%”
April 19, 2019
Ian Stewart posted a reply to If x is an integer, then which of the following statements in the Problem Solving forum
“Lots of ways to do this, for example: x^2 - x - 1 = x(x-1) - 1 Notice x(x-1) is the product of two consecutive integers, so it is the product of one odd and one even integer, and must therefore be even. When we subtract 1 from this product, we get an odd number, so x(x-1) - 1 is odd.”
April 19, 2019
Ian Stewart posted a reply to A number of oranges are to be distributed evenly among a in the Data Sufficiency forum
“Statement 1 is automatically true, so it really only tells us that it is possible to divide the number of baskets by 2. But we might have 2 baskets with 10 oranges each, or 20 baskets with 1 orange each, for example, so that information is not sufficient. If Statement 2 is true, then when we ...”
April 19, 2019
Ian Stewart posted a reply to From a group of \(J\) employees, \(K\) will be selected, at in the Data Sufficiency forum
“Using only Statement 1, we might be picking only from 15 employees in total, in which case it''s not likely, but also not nearly impossible, that Lisa and Philip sit together. But we might be picking from 15,000,000 employees in total, and the probability might be almost zero that we even pick Lisa ...”
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
GMATGuruNY posted a reply to Verb-ing doubt in the Sentence Correction forum
“NOUN + VERBing implies that the VERBing is a restrictive modifier. The purpose of a restrictive modifier is to SPECIFY the type of noun being discussed. Here, the restrictive modifier in blue implies the following: There are many types of planets. The sentence is not referring to all these ...”
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
GMATGuruNY posted a reply to If x and y are positive integers and in the Data Sufficiency forum
“Statement 1: x=2 \(2^y =2^{2y-3} \) Since each side has the same base, the two exponents must be equal: y = 2y-3 3 = y Since the values of x and y are known, the value of \(x^y\) can be determined. SUFFICIENT. Statement 2: Thus, x=2. Same information as in Statement 1. Since Statement ...”
April 17, 2019
GMATGuruNY posted a reply to There are 10 employees in an office. The table shows how in the Problem Solving forum
“List of 10 pet values implied by the chart: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3 Since the answer choices are all 3 or greater, the addition of the manager''s pet value will yield the following list of 11 values: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, M Since the new average must be equal to the median value ...”
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
GMATGuruNY posted a reply to Computer-based activities in the Critical Reasoning forum
“In a strengthen CR, the OA SUPPORTS THE PASSAGE. In an inference CR, the PASSAGE SUPPORTS THE OA. Here, the OA supports the passage. The result is a strengthen CR. Since the OA supports the conclusion, its negation naturally will weaken the conclusion.”
April 16, 2019
GMATGuruNY posted a reply to OG Most of the country's biggest daily newspapers in the Sentence Correction forum
“This is the comparison conveyed by the green sentence above. Here, each blue portion has a subject (the company) and a verb (had) and thus constitutes a clause. The result is a logical comparison. This is the comparison implied by the incorrect red sentence above. The first blue portion ...”
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
GMATGuruNY posted a reply to Three salespeople, Dan, Matt, and Nicole, earned annual in the Problem Solving forum
“D:M:N = 3:5:8. The sum of the parts of the ratio = 3+5+8 = 16. The values in red indicate the following: Nicole''s fraction of the total = 8/16 = 1/2. Since Nicole''s $28,000 is 1/2 of the total, the total = $56,000. The correct answer is E.”
April 15, 2019
GMATGuruNY posted a reply to Together, 15 type A machines and 7 type B machines can in the Problem Solving forum
“Let the job = 44 units. Since 15A+7B take 4 hours to complete the 44-unit job, the rate for 15A+7B = w/t = 44/4 = 11 units per hour. Since 8B+15C take 11 hours to complete the 44-unit job, the rate for 8B+15C = w/t = 44/11 = 4 units per hour. Adding together 15A+7B=11 and 8B+15C=4, we get: ...”
April 15, 2019
GMATGuruNY posted a reply to Mark has fewer than 9 coins. Each coin is either a quarter in the Data Sufficiency forum
“Statement 1: 25Q + 10D = 170 5Q + 2D = 34 To minimize the number of coins, we must maximize the value of Q. If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34. In this case, the total number of coins = 6+2 = 8. If the value of Q decreases, then the total number of coins ...”
April 15, 2019
GMATGuruNY posted a reply to 12^(1/2) + 108^(1/2) + 48^(1/2) = in the Problem Solving forum
“√12 + (√9 * √12) + (√4 * √12) = √12 + 3√12 + 2√12 = 6√12 = 6 * √4 * √ 3 = 12√3 The correct answer is A.”
April 15, 2019
GMATGuruNY posted a reply to If n is a positive integer greater than 6, what is the in the Data Sufficiency forum
“Approach 1: Since n is greater than 6, and the statements refer to n², make a list of perfect squares greater than 6²: n² = 49, 64, 81, 100, 121, 144, 169, 196, 225. Subtracting 1 from these values, we get the following options for n² - 1: n² - 1 = 48, 63, 80, 99, 120, 143, 168, 195, ...”
April 15, 2019
GMATGuruNY posted a reply to Which of the following is equivalent to in the Problem Solving forum
“Let x=2 and y=1, with the result that (x+y)/3 - (x-y)/4 = 1 - 1/4 = 3/4. The correct answer must yield 3/4 when x=2 and y=1. Only D works: (7y+x)/12 = (7*1 + 2)/12 = 9/12 = 3/4 The correct answer is D.”
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
GMATGuruNY posted a reply to In a certain office, 50 percent of the employees are college in the Data Sufficiency forum
“Let T = the total number of employees. Since 60% of the employees are over 40, we get: Over 40 = 0.6T 30% of those over 40 -- in other words, 30% of the expression in blue -- have master''s degrees. Thus: Over 40 with master''s = 0.3(0.6T). To calculate the value of the expression in ...”
April 14, 2019
GMATGuruNY posted a reply to Dwight and Mose decide to build a new barn on their farm, in the Problem Solving forum
“Every time Dwight does 1/4 of the remaining work, 3/4 of the work remains. Every time Mose does 1/6 of the remaining work, 5/6 of the work remains. When Mose starts his third shift, Dwight has completed 3 shifts, while Mose has completed 2 shifts. Thus, the remaining work at the start of Mose''s ...”
April 14, 2019
GMATGuruNY posted a reply to In a law firm, 72% of the employees are associates and 54% in the Problem Solving forum
“Let the total number of employees = 100, implying that the total number of associates = 72% of 100 = 72 and that the number of senior associates = 54% of 100 = 54. The prompt should make clear that every associate is either a junior associate or senior associate, yielding the following equation: ...”
April 14, 2019
GMATGuruNY posted a reply to A library branch originally contained 18360 volumes, 30% of in the Problem Solving forum
“Since the answer choices are PERCENTS, the total number of books can be ANY POSITIVE VALUE. 30% = 3/10, implying a denominator of 10. Let the total number of books = the product of the three denominators 10, 3 and 3 = 10*3*3 = 90. Since 30% of the books are fiction, the number of fiction books ...”
April 12, 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
GMATGuruNY posted a reply to Heavy commitment by an executive in the Sentence Correction forum
“that-clause includes its own subject and verb and thus does not require an additional agent. In the blue that-clause above, the subject for will meet (verb) is a system of import relief laws. Since it is clear that A SYSTEM will meet the strategic needs, no additional agent is required. An ...”
April 11, 2019
GMATGuruNY posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum
“Since Mary is behind Kate by 250 meters -- half the circumference of the track -- she will catch up to Mary when she has traveled 250 meters more than Kate. To catch up to Kate a second time, Mary must then travel one more lap than Kate -- in other words, 500 meters more than Kate. Implication: ...”
April 11, 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
GMATGuruNY posted a reply to Heavy commitment by an executive in the Sentence Correction forum
“The bad weather makes it difficult to work outdoors. Here, the infinitive in blue is not immediately preceded by an agent: the sentence does not specify WHO is intended TO WORK. The implication is that the agent for the blue infinitive is not a specific person but people IN GENERAL, as follows: ...”
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
GMATGuruNY posted a reply to How many rectangles are found in the lattice below? in the Problem Solving forum
“https://i.postimg.cc/Z0xg3MXX/lattice.png To form a rectangle, we must combine as HORIZONTAL LENGTH with a VERTICAL LENGTH: Horizontal length: Number of ways to choose a horizontal length of 1: AB, BC, CD, DE, EF = 5 Number of ways to choose a horizontal length of 2: AC, BD, CE, DF = 4 ...”
April 9, 2019
GMATGuruNY posted a reply to If x is a positive integer, is the remainder 0 when in the Data Sufficiency forum
“\(3^x + 1\) will yield a remainder of 0 when divided by 10 if it has a units digit of 0. 3¹ --> units digit of 3. 3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.) 3³ --> units digit of 7. (Since the product of the preceding units digit and ...”
April 9, 2019
GMATGuruNY posted a reply to If d is a positive integer and f is the product of the first in the Data Sufficiency forum
“30! = 30*29*28*....*3*2*1. Statement 1: To determine the greatest possible value for d, we need to know the number of 10''s contained within 30! Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 30! will yield a 10. The prime-factorization of 30! is composed ...”
April 9, 2019
GMATGuruNY posted a reply to Last year, the price of a jar of peanut butter at a certain in the Problem Solving forum
“The price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. Let P = 10 and J = 20 This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20% New P = 10 + (20% of 10) = 10 + ...”
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
GMATGuruNY posted a reply to If the median and average (arithmetic mean) of a set of 4 di in the Data Sufficiency forum
“In ascending order, let the four numbers = a, b, c, d. Since the average of the 4 numbers = 10, we get: (a+b+c+d)/4 = 10 a+b+c +d = 40 Since the median of the 4 numbers = 10, we get: (b+c)/2 = 10 b+c = 20 Subtracting the blue equation from the red equation, we get: (a+b+c+d) - (b+c) = 40-20 ...”
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
GMATGuruNY posted a reply to Mixture A is 15 percent alcohol, and mixture B is 50 percent in the Problem Solving forum
“A = 15% alcohol B = 50% alcohol The MIXTURE of A and B = 30% alcohol To determine the ratio of A to B, use ALLIGATION -- a very efficient way to handle mixture problems. Step 1: Plot the 3 percentages on a number line, with the percentages for A and B (15% and 50%) on the ends and the ...”
April 7, 2019
GMATGuruNY posted a reply to A museum sold 30 tickets on Saturday. Some of the tickets so in the Data Sufficiency forum
“Let G = the number of general tickets. Since a total of 30 tickets are sold, the number of special exhibit tickets = 30-G. Since general tickets = $10 each and special exhibit tickets = $70 each, we get: Total revenue = 10G + 70(30-G) = 10G + 2100 - 70G = 2100 - 60G. Statement 1: 1570 < ...”
April 7, 2019
GMATGuruNY posted a reply to If 500 is the multiple of 100 that is closest to X and 400 in the Data Sufficiency forum
“Statements combined: Case 1: X=460, with the result that 500 is the multiple of 100 closest to X Y=360, with the result that 400 is the multiple of 100 closest to Y In this case, X+Y=820, so the multiple of 100 closest to X+Y is 800. Case 2: X=490, with the result that 500 is the multiple of ...”
April 7, 2019
Ian Stewart posted a reply to Harry and Ron work for the same company but earn different in the Data Sufficiency forum
“Say Harry earns $H, and has $E in expenses, while Ron earns $R, and spends $S. Then Harry saves H-E dollars, and Ron saves R-S dollars. Statement 1 tells us: H + S > R + E H - E > R - S or in other words, Harry''s savings exceed Ron''s savings. Now, it''s not clear what is meant ...”
April 6, 2019
Ian Stewart posted a reply to n is a positive integer greater than 2. If y = 9^0 + 9^1+ in the Data Sufficiency forum
“If you look at the units digits of various powers of 9, you''ll see they alternate between 1 and 9: 9^0 ends in 1 9^1 ends in 9 9^2 ends in 1 9^3 ends in 9 and so on. So if we add 9^0 + 9^1 + 9^2 + ... + 9^n, we''ll get something ending in 0 when n is even, and something ending in 1 when n ...”
April 6, 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
GMATGuruNY posted a reply to One legacy of Madison Avenue's in the Sentence Correction forum
“Generally, a when-clause refers to an action performed at a particular moment: When Mary entered the room, John smiled. Here, the usage of when implies that the action in blue happened at a particular moment. An as-clause refers to an action performed over an extended period of time: Adam sang ...”
April 6, 2019
GMATGuruNY posted a reply to The 32 species that make up the dolphin family are closely r in the Sentence Correction forum
“There is no reason to repeat which in the OA. Even if more than one verb is attributed to COMMA + WHICH, the usage of one which should suffice.”
April 6, 2019
GMATGuruNY posted a reply to In a nationwide poll, N people were interviewed. If 1/4 in the Problem Solving forum
“Let N=12. Number who answered yes to question 1 = (1/4)12 = 3. Number who also answered yes to question 2 = (1/3)3 = 1. Number who didn''t answer yes to both questions = 12-1 = 11. This is our target. Now we plug N=12 into the answers to see which yields our target of 11. Only E works: ...”
April 6, 2019
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
Ian Stewart posted a reply to Is BG > EC? in the Data Sufficiency forum
“BG is the height of triangle ABC (when we use AC as our base), and EC is the height of triangle DEF (when we use DF as our base). It''s confusing to use all those capital letters, so let''s use ''h'' for the height BG, and ''j'' for the height EC. We also have three important lengths along the ...”
April 6, 2019
Ian Stewart posted a reply to If a certain positive integer is divided by 9, the ..... in the Data Sufficiency forum
“Statement 1 tells us our number is 30 greater than some multiple of 45, so our number is equal to 45q + 30, for some integer q. But 45q + 30 = 5(9q + 6), which is clearly divisible by 5, so the remainder is 0 when we divide our number by 5, and Statement 1 is sufficient, even without using any ...”
April 6, 2019
Ian Stewart posted a reply to In the figure above, if the length of MO is 10 in the Data Sufficiency forum
“If you knew that the seemingly-vertical line of length ''h'' was at right angles to the line MO, then it would be easy, with both statements, to use Pythagoras to find the lengths of all of the sides. But without knowing if we have a right angle there, we can''t do much, and the answer is E. ...”
April 5, 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
GMATGuruNY posted a reply to Is x < 0? in the Data Sufficiency forum
“Statement 1: x³ < -1 The cube of x will be negative only if x itself is negative. Thus, x < 0. SUFFICIENT. Statement 2: x³ + x < -1 x(x² + 1) < -1 Since the square of a value cannot be negative, x² ≥ 0, with the result that the factor in blue must be POSITIVE. ...”
April 5, 2019
GMATGuruNY posted a reply to A pizza shop sold small pizzas for $4.5 in the Problem Solving forum
“The GMAT would list the answer choices in ascending or descending order, as follows: We can PLUG IN THE ANSWERS, which represent the number of small pizzas. The average cost per pizza = 5050/500 ≈ $10. Since the average cost ($10) is much closer to the price of a large pizza ($12.50) than ...”
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
GMATGuruNY posted a reply to Fossils of feathered dinosaurs - GMAT prep Exam pack 1 in the Sentence Correction forum
“A general truth is something that is true not just at a particular moment but is true IN GENERAL. Mary plays the saxophone. Here, the portion in blue expresses a general truth about Mary. To express a GENERAL TRUTH, we use the simple present tense. The SC above is intended to express a general ...”
April 2, 2019
GMATGuruNY posted a reply to While making a non-stop trip, a bus averaged m mph for the in the Data Sufficiency forum
“Distance traveled in the first 5 hours = 5m. Distance traveled in the remaining 4 hours = 4n. Average speed for the entire 9-hour trip = (5m + 4n)/9. To determine the average speed for the entire trip, we need to know the value of 5m+4n. Question stem, rephrased: What is the value of 5m+4n? ...”
April 2, 2019
GMATGuruNY posted a reply to OG13 - Q20 in the Sentence Correction forum
“The OA does not make a comparison. to double X = to increase X by 100% OA: Personal spending in the Julv-September quarter would more than double the...growth rate. Conveyed meaning: Personal spending in the July-September quarter would increase the growth rate by more than 100%.”
April 2, 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
GMATGuruNY posted a reply to OG12, Q18 in the Sentence Correction forum
“OA: Plants are more efficient than fungi at acquiring carbon, in the form of carbon dioxide. Here, the modifier in green is an adverb in that it describes UNDER WHAT CIRCUMSTANCE the preceding blue action happens. Under what circumstance ARE plants MORE EFFICIENT at acquiring carbon? Under the ...”
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
GMATGuruNY posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum
“Let B = Barry''s rate and W = the walkway''s rate. The distance can be ANY VALUE. Let the distance = 240 meters. WITH the walkway, the time = 30 seconds: Here, Barry and the walkway WORK TOGETHER, so we ADD their rates: B+W = d/t = 240/30 = 8 meters per second. AGAINST the walkway, the ...”
April 1, 2019
Ian Stewart posted a reply to What is the value of 10^x · 10^y? in the Data Sufficiency forum
“I imagine there''s a typo in the question somewhere, because as written, the statements aren''t consistent, and the answer is not D (it would be A). It seems more likely the question is meant to say something like: What is $$10^x 10^y$$ ? 1. 2^(x+y) = 16 2. 5^(x+y) = 625 Since 10^x * 10^y ...”
April 1, 2019
Ian Stewart posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum
“If s is his speed, and w the speed of the walkway, then when he walks with the walkway, his net speed is s+w, and when he walks against the walkway, his net speed is s-w. Using the familiar S = D/T equation for both cases, we have: s+w = 30/30 = 1 s-w = 30/120 = 1/4 and adding these two ...”
April 1, 2019
Ian Stewart posted a reply to For any given x and any positive integer n in the Problem Solving forum
“For any sequence question, it is usually a good idea to work out the first few terms until you understand the structure of the sequence. Here, if s_n = x^(2n - 1) then plugging in n =1, 2 and 3 we find: s_1 = x^1 s_2 = x^3 s_3 = x^5 and so on. We want to multiply these terms together, ...”
April 1, 2019
Ian Stewart posted a reply to For positive integers n, the integer part of the nth term in the Problem Solving forum
“The digits long after the decimal point are not going to matter here, since they only make a minuscule contribution to the sum, and we only need a rough estimate. If we work out the first seven terms, truncating each to one decimal place, we have: 1.2 2.4 3.6 4.8 5.1 6.1 7.1 When we ...”
April 1, 2019
Ian Stewart posted a reply to Is xy > 0? in the Data Sufficiency forum
“xy > 0 will be true if x and y have the same sign, so if both are positive, or if both are negative. x^2 is always positive or zero, so Statement 1 tells us almost nothing (it only tells us x is not zero). In Statement 2, we can divide by y^2 on both sides, because we know y^2 is positive (so ...”
April 1, 2019
Ian Stewart posted a reply to Is the slope of line z positive? in the Data Sufficiency forum
“If two lines are perpendicular, their slopes are negative reciprocals, so if one line has a slope of m, the other has a slope of -1/m. So from Statement 1, if line m has a slope of -1/4, the perpendicular line z must have a slope of 4, and Statement 1 is sufficient. Knowing about one point on a ...”
April 1, 2019
GMATGuruNY 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
“2⁸ = 256 2⁷ = 128 Thus: 2⁸ + 2⁷ + 2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2 + 2 = 256 + 128 + (around 100) ≈ 500. Only A is viable: 2⁹ = 512. The correct answer is A.”
April 1, 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
Ian Stewart posted a reply to Points (a, b) and (c, d) lie on line L in the coordinate in the Data Sufficiency forum
“When you subtract y-coordinates of two points, you''re just finding the distance between them purely in the vertical direction. That''s sometimes called the "rise". Similarly when you subtract x-coordinates of two points, you''re finding the purely horizontal distance between them, ...”
March 31, 2019
Ian Stewart posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum
“Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.”
March 31, 2019
Ian Stewart posted a reply to Alice bought a certain number of 30 cent stamps, 35 cent in the Data Sufficiency forum
“Using Statement 2 alone, if she bought x stamps at 30 cents, and x stamps at 40 cents, she spent 70x cents in total just on those stamps. If she only spent 420 cents overall, then x clearly is no greater than 6. But if she also bought some 35 cent stamps, x must be strictly less than 6. And ...”
March 31, 2019
Ian Stewart posted a reply to If \(n\) is a positive integer and \(r\) is the remainder in the Data Sufficiency forum
“n-1, n and n+1 are three consecutive integers. If, as Statement 1 tells us, n is odd, then n-1 and n+1 are both even -- in fact, they are consecutive even numbers. If you take any two consecutive even integers, one of them will always be a multiple of 4, so Statement 1 guarantees that (n-1)(n+1) is ...”
March 31, 2019
Ian Stewart posted a reply to How many hours did it take Helen to drive from her house to in the Data Sufficiency forum
“Statement 1 is clearly insufficient. Using Statement 2, maybe her speed was 8 km/hr, and the total distance was 16 km, so took 2 hours. Then if her speed was 8 km/hr greater, so was 16 km/hr, she would have saved an hour. But we know there must also be a solution where her speed was 72 km/hr, ...”
March 31, 2019
Ian Stewart posted a reply to In the diagram above, O is the center of the circle and ACDE in the Data Sufficiency forum
“If you connect a diameter of a circle to a point C on the circle, you always form a right angle at C, so Statement 2 tells us nothing new, and is useless. Using only Statement 1, since we know we have a right triangle, and we know two of its sides (the hypotenuse is twice the radius, so is 4), we ...”
March 31, 2019
Ian Stewart posted a reply to In the figure above, all angles are right angles. If the len in the Data Sufficiency forum
“The perimeter of the figure is identical to the perimeter of a rectangle with sides a and b (if you just draw the two lines in the top right corner that you''d need to draw to make that rectangle, you''ll see that you''re adding a line of length v to the top side, and a line of length u to the ...”
March 31, 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
GMATGuruNY posted a reply to Cars emerging from a motorway arrive at a junction that in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the number of cars in the left lane. Answer choice C: 1700 If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane ...”
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
GMATGuruNY posted a reply to A 3-character alpha-numeric code does have the following in the Problem Solving forum
“Number of options for the first character = 8. (Of the 10 digits, any digit but 0 or 9.) Number of options for the second character = 24. (Of the 26 letters in the alphabet, any but a or z.) Number of options for the third character = (number of options for the first character) + (number of ...”
March 29, 2019
GMATGuruNY posted a reply to The ratio of boys to girls in Class A is 3 to 4. The ratio in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the number of girls in Class A. Since b:g = 3:4, the number of girls must be a multiple of 4. Eliminate B, C and D. Answer choice A: g = 8. Since b:g = 3:4 = 6:8, b=6. Since Class A has one more boy and two more girls than Class B, in Class B, ...”
March 29, 2019
GMATGuruNY posted a reply to 100 students appeared for two tests-Maths and English. For in the Data Sufficiency forum
“100 = Only Math + Only English + Both + Neither For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. Let B = both, implying that Only Math = 8B and that Only English = 9B. Thus: 100 = 8B + 9B + B + Neither 100 = 18B + Neither ...”
March 28, 2019
GMATGuruNY posted a reply to An optometrist charges $150 per pair for soft contact lenses in the Problem Solving forum
“Since $150 soft lenses and $85 hard lenses yield $1690 in revenue, we get: 150S + 85H = 1690 30S + 17H = 238 The sum on the left side must yield a units digit of 8. Since 17*4 = 68, it is likely that H=4: 30S + 17*4 = 338 30S + 68 = 238 30S = 170 S=9 S=9 and H=4 satisfy the condition ...”
March 28, 2019
GMATGuruNY posted a reply to OG-12 SC Q-43 Laos has a land area in the Sentence Correction forum
“D: Laos has a land area comparable to the size of Great Britain, but only four million in population, and many are members of hill tribes ensconced in the virtually inaccessible mountain valleys of the north. Error 1: The intent here is to compare the LAND AREA of Laos to the LAND AREA of Great ...”
March 28, 2019
GMATGuruNY posted a reply to Which of the following is the solution set for the inequalit in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the range of x. A: -1 < x < 0 Plugging x=-0.5 into the given inequality, we get: 0 < |-0.5| - 2(-0.5) < 3 0 < 0.5 + 1 < 3 0 < 1.5 > 3 Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its ...”
March 28, 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
GMATGuruNY posted a reply to A straight highway connects two cities P and Q, and goes via in the Data Sufficiency forum
“Statement 1: For every 2 hours spent at 30 mph and 1 hour spent at 50 mph, 3 hours are spent at 60 mph. Average speed per 6 hours = (2*30 + 1*50 + 3*60)/6 = 290/6. SUFFICIENT. Statement 2: Case 1: NQ = 180 miles, PM = 60 miles and MN = 50 miles Since NQ is traveled at 60 mph, the time for ...”
March 27, 2019
GMATGuruNY posted a reply to Geometry in the Problem Solving forum
“https://i.postimg.cc/N2Ky6DSp/square-divided-into-triangles.png Each triangle in the figure above is an isosceles right triangle with sides 1, 1 and √2. Shaded region = 4 triangles. Largest square = 16 triangles. Thus: (shaded region)/(largest square) = 4/16 = 1/4. The correct answer is ...”
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
GMATGuruNY posted a reply to A music festival took place over two days, Saturday and in the Data Sufficiency forum
“Anyone who attended the festival must have attended only Saturday, only Sunday, or both days. Let the total number of attendees = 100. Statement 1: 40% of attendees attended both days. No way to determine how many attendees attended only Saturday. INSUFFICIENT. Statement 2: 70% of attendees ...”
March 26, 2019
GMATGuruNY posted a reply to Boat World sells a certain boat and a certain trailer. What in the Data Sufficiency forum
“Let b = boat and t = trailer. What is the value of t? Statement 1: b = 7500+t No way to solve for t. INSUFFICIENT. Statement 2: b+t = 15000 No way to solve for t. INSUFFICIENT. Statements combined: Since we have two variables (b and t) and two distinct linear equations (b=7500+t and ...”
March 26, 2019
GMATGuruNY posted a reply to p, q, and r are different prime numbers. What is the value o in the Data Sufficiency forum
“Statement 1: (pq)² = 36 pq = 6 Case 1: p=2 and q=3 Case 2: p=3 and q=2 Since q can be different values, INSUFFICIENT. Statement 2: (qr)² = 225 qr = 15 Case 1: q=3 and r=5 Case 2: q=5 and r=3 Since q can be different values, INSUFFICIENT. Statements combined: Only one case ...”
March 26, 2019
GMATGuruNY posted a reply to √r + 2/√r = 4. What is the value of r + 4/r? in the Problem Solving forum
“(a+b)² = a² + b² + 2ab √r + 2/√r = 4 (√r + 2/√r)² = 4² (√r)² + (2/√r)² + 2(√r)(2/√r) = 16 r + 4/r + 4 = 16 r + 4/r = 12 The correct answer is A.”
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
Ian Stewart posted a reply to There are x people and y chairs in a room where x and y are in the Data Sufficiency forum
“This question doesn''t make any sense, at least if the OA is A. I can guess the logic they use to justify ''A'' as the right answer -- using only Statement 1, there are only two primes that sum to 12, namely 5 and 7. If we want to seat 5 people in 7 chairs, there are 7*6/2! = 21 ways to choose the ...”
March 25, 2019
GMATGuruNY posted a reply to How many trailing zeroes would be found in 63! upon in the Problem Solving forum
“TRAILING 0''s = the number of 0''s at the end of a large product. 63! = 63*62*61*....*3*2*1. Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 63! will yield a 0 at the end of the integer representation of 63!. The prime-factorization of 63! includes FAR ...”
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
GMATGuruNY posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum
“Let r=100 cents. For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars. Let x = 2 miles. Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars. With a 50% discount, the cost in dollars = 3. This is our target. Now we plug x=2 and r=100 into the answers to see which ...”
March 25, 2019
GMATGuruNY posted a reply to 60% of all students in a class commute by public in the Problem Solving forum
“Use a DOUBLE-MATRIX to organize the data. Let P = public transportation, NP = not public transportation, S = science, NS = not science. 60% of all students in a class commute by public transportation. 30% of the students aspire to be scientists. The following matrix is yielded: ...”
March 25, 2019
GMATGuruNY posted a reply to GPREP SC-8 in the Sentence Correction forum
“Proposed revision: The sandpipers...are a result of residential and industrial development. This meaning is nonsensical. BIRDS cannot be a RESULT. This line of reasoning is valid: In D and E, the referent for in the northeastern United States is unclear.”
March 24, 2019
Ian Stewart posted a reply to Time and work in the Problem Solving forum
“You can do this mathematically - if you suppose it takes t minutes for A to print n pages, you can then get the same time for each machine: A prints 2n pages in 2t minutes B prints n pages in 2t minutes so A+B together print 3n pages in 2t minutes and A+B together print n pages in 2t/3 ...”
March 24, 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
GMATGuruNY posted a reply to If P and Q are positive integers, and if P > 1, does P = in the Data Sufficiency forum
“Statement 1: Case 1: P=2 and Q=2, with the result that P divides evenly into Q In this case, P=Q, so the answer to the question stem is YES. Case 2: P=2 and Q=4, with the result that P divides evenly into Q In this case, P≠Q, so the answer to the question stem is NO. INSUFFICIENT. ...”
March 24, 2019
GMATGuruNY posted a reply to Is it true that x > 0? in the Data Sufficiency forum
“Statement 1: Case 1: x=0 In this case, the answer to the question stem is NO. Case 2: x≠0, allowing us to divide both sides by x x²/x = 2x/x x = 2 In this case, the answer to the question stem is YES. INSUFFICIENT. Statement 2: Case 1: x=0 In this case, the answer to the question ...”
March 24, 2019
Ian Stewart posted a reply to A number of ties are individually packaged in unmarked boxes in the Data Sufficiency forum
“It makes no logical sense to ask a DS question like this, because it''s not clear what information would be sufficient to find the "maximum number" of something. That''s easy to see if you imagine a different question: There are 25 boxes, and each box contains one colored tie. What is ...”
March 23, 2019
Ian Stewart posted a reply to At a particular business school which requires applicants to in the Data Sufficiency forum
“You can say "the average score of admitted applicants was 15 points higher than of rejected applicants" or you can say "the difference between the average score of accepted applicants and rejected applicants was 15 points" but you can''t say both things in the same sentence. The ...”
March 23, 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
GMATGuruNY posted a reply to Events A and B are independent and have equal probabilities in the Data Sufficiency forum
“Statement 1: P(at least one event occurs) = 1 - P(neither event occurs) Thus: P(at least A or B) = 1 - P(neither A nor B) Since P(at least A or B) = 0.84, we get: 0.84 = 1 - P(neither A nor B) P(neither A nor B) = 0.16 P(not A) * P(not B) = 0.16. Since it is given that P(A) = P(B), P(not ...”
March 23, 2019
GMATGuruNY posted a reply to In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, in the Problem Solving forum
“Third-side rule: The third side a triangle must be LESS THAN THE SUM OF and GREATER THAN THE DIFFERENCE OF the other two sides. Here, all the sides must be INTEGER values. In triangle ANS, AS=10 and NS=5. Thus, third side AN must be an integer value less than 10+5 = 15 and greater than 10-5 = ...”
March 23, 2019
Ian Stewart posted a reply to Find the range of values of \(x\) that satisfy the in the Problem Solving forum
“(x+1)(x-2) > 4 x^2 - x - 2 > 4 x^2 - x - 6 > 0 (x-3)(x+2) > 0 So either x-3 and x+2 are both positive, which will be true when x > 3, or both x-3 and x+2 are negative, which will be true when x < -2.”
March 22, 2019
Ian Stewart posted a reply to If \(xy \neq 0\) and \(2x + 3y\) is equal to 175 percent in the Problem Solving forum
“If we''re taking 175% of something, we''re multiplying it by 1.75, or by 7/4. So 2x + 3y = (7/4)(8x) 2x + 3y = 14x 3y = 12x 1/4 = x/y”
March 22, 2019
Ian Stewart posted a reply to The largest bonus that Felix can receive this year is equal in the Data Sufficiency forum
“His smallest bonus is 30% of 20% of his salary, so, multiplying, is 6% of his salary. Statement 1 tells us his smallest bonus, and since we know that''s 6% of his salary, we can find his salary. Statement 2 tells us the difference in his largest and smallest bonuses, and since 20% - 6% = 14%, that ...”
March 22, 2019
Ian Stewart posted a reply to Paul, a painter, paints only flowers or cats in his notebook in the Data Sufficiency forum
“Am I missing something? Statement 2 tells us the exact answer to the question. I assume it means to ask how many *cat* pictures in charcoal there are. Since we know the 39 pictures mentioned in the stem consist precisely of flower-pencil, flower-charcoal, and cat-charcoal pictures, then once we ...”
March 22, 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
GMATGuruNY posted a reply to Express 2^20-2^19-2^18-2^17 as a power of 2. in the Problem Solving forum
“Test an analogous case with easier values: 2⁴ - 2³ - 2² - 2¹ = 16 - 8 - 4 - 2 = 2¹ The matching blue portions imply the following: 2²⁰ - 2¹⁹ - 2¹⁸ - 2¹⁷ = 2¹⁷ The correct answer is C.”
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
GMATGuruNY posted a reply to If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? in the Problem Solving forum
“(r + 1/r)² = 5 r + 1/r = √5 (r + 1/r)² = 5 r² + 1/r² + 2(r)(1/r) = 5 r² + 1/r² + 2 = 5 r² + 1/r² = 3 Multiplying the blue equation and the red equation, we get: (r² + 1/r²)(r + 1/r) = 3√5 r³ + (r²)(1/r) + (1/r²)(r) + 1/r³ = 3√5 r³ + (r + 1/r) + 1/r³ = 3√5 ...”
March 21, 2019
GMATGuruNY posted a reply to A dessert recipe calls for 50% melted chocolate and 50% in the Problem Solving forum
“Chocolate percentage in the incorrect sauce: 40%. Chocolate percentage in the pure chocolate: 100%. Chocolate percentage in the mixture: 50%. Let I = the incorrect sauce and C = the pure chocolate. The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. ...”
March 21, 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
GMATGuruNY posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill in the Problem Solving forum
“Downhill speed - uphill speed = (x+10) - (x-8) = 18. Implication: The downhill speed is 18 mps greater than the uphill speed. We can PLUG IN THE ANSWERS, which represent the downhill speed. Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...”
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
GMATGuruNY posted a reply to Jeremiah invests his savings of $120,000 by dividing it in the Problem Solving forum
“On the GMAT, compounded interest is typically just a bit more than simple interest. Since the answer choices are all greater than 2% -- the percentage given in the prompt -- they must represent the HIGHER interest rate, with 2% representing the LOWER interest rate. Lower rate: Since 3/4 of ...”
March 21, 2019
GMATGuruNY posted a reply to If m and n are positive integers, is m+n divisible by 15? in the Data Sufficiency forum
“Rule: MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X 225 = 9*25 Statements combined: Case 1: m=9 and n=25*15, with the result that m is a multiple of 9, n is a multiple of 15, and mn = 9*25*15 = 225*15 = multiple of 225 In this case, m+n ...”
March 21, 2019
GMATGuruNY posted a reply to What is the smallest positive integer n such that n / 420 ca in the Problem Solving forum
“A fraction will yield a terminating decimal if the prime-factorization of its denominator contains only 2''s and/or 5''s. n/420 = n/(2*2*3*5*7). For a terminating decimal to be yielded, the prime factors in red must CANCEL OUT with n, leaving only 2''s and 5''s in the denominator. Thus, the ...”
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
GMATGuruNY posted a reply to The consultant explained that companies in the Sentence Correction forum
“Generally, a one-word adverb such as tirelessly will not be positioned between a verb and its direct object. Incorrect: Companies lobby tirelessly government officials. Here, tirelessly (adverb) is awkwardly positioned between lobby (verb) and government officials (direct object). Correct: ...”
March 20, 2019
GMATGuruNY posted a reply to one another vs. others? in the Sentence Correction forum
“Some grammarians -- including me -- reserve each other for two elements and one another for more than two. Other grammarians consider the two modifiers interchangeable. A club has exactly three members: Ann, Beth, and Carol. The sentence above implies the following: Ann, Beth and Carol ...”
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
GMATGuruNY posted a reply to If arc PQR above is a semicircle, what is the length of diam in the Data Sufficiency forum
“An INSCRIBED ANGLE is formed by two chords. Thus, angle PQR is an inscribed angle. An inscribed angle that intercepts the diameter is a RIGHT ANGLE. Thus, angle PQR is a right angle, implying that triangle PQR is a RIGHT TRIANGLE. http://s15.postimage.org/xozmfjdh3/PQR.jpg In the figure ...”
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
GMATGuruNY posted a reply to Reiko drove from point A to point B at a constant speed, and in the Data Sufficiency forum
“Test the THRESHOLD. Since we want to know whether the speed from A to B is greater than 40mph, the threshold here is 40mph. Statement 1: Reiko''s average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour. Let the distance in each direction = 40 ...”
March 19, 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
GMATGuruNY posted a reply to Danny spends $360 buying his favorite dolls. If he buy only in the Problem Solving forum
“Since a small doll costs $1 less than a large doll, the answer choices imply the following options for the price of a small doll: 4 5 6.2 7 8 Given that all of the values in the prompt are INTEGERS, the price of a small doll is almost certain to be a factor of 360. Only the values in blue ...”
March 18, 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
Ian Stewart posted a reply to If $ defines a certain operation, is p $ q less than 20? in the Data Sufficiency forum
“Statement 1 tells us that we want to know if 2p^2 - q is less than 20, which we can''t tell with no information about p or q. Statement 2 is clearly not sufficient alone, because we have no idea what this "$" operation does. Using both Statements, we can clearly evaluate p$q = 2p^2 - q and ...”
March 18, 2019
Ian Stewart posted a reply to List S and List T each contain 5 positive integers, and for in the Data Sufficiency forum
“Since we know three values in List S, and we know the mean, and thus the sum, of all five values in List S, then if we''re given a fourth value in list S, we can find the fifth missing value. So from Statement 1 alone, we know exactly what List S contains. Similarly, from Statement 2 alone, we know ...”
March 18, 2019
Ian Stewart posted a reply to Is xy an integer? (1) x is the ratio of the area of a squar in the Data Sufficiency forum
“Strange question - you obviously need to know about both x and y, so neither statement could be sufficient alone. But Statement 1 gives us the value of x, and Statement 2 gives us the value of y, so of course we can answer any question in the universe about x and y using both Statements, and the ...”
March 18, 2019
GMATGuruNY posted a reply to Of the 25 cars sold at a car dealership, some had auto trans in the Data Sufficiency forum
“The following cases satisfy both statements: Case 1: 2 cars have neither 1 car has both antilock breaks and automatic transmission 22 cars have only automatic transmission. Case 2: 2 cars have neither 22 cars have both antilock breaks and automatic transmission 1 car has only automatic ...”
March 18, 2019
GMATGuruNY posted a reply to A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 in the Problem Solving forum
“Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color: 3 red 4 green 4 yellow 4 blue 4 white Sum = 3+4+4+4+4 = 19 Implication: It is possible to remove 19 balls without selecting 5 of the same color. ...”
March 18, 2019
Ian Stewart posted a reply to A carpenter worked alone for 1 day on a job that would take in the Problem Solving forum
“Once the first day is done, 6/7 of the job is left. We then know that the two workers together do 6/7 of a job in 4 days. So now we know these two things: Carpenter A does 1 job in 7 days Carpenters A+B together do 6/7 jobs in 4 days We can now get the same time for both: A does 4 jobs ...”
March 17, 2019
Ian Stewart posted a reply to What is the smallest positive integer \(x\) such that in the Problem Solving forum
“Prime factorize the 450: 450 = 50*9 = 2 * 3^2 * 5^2 To get a perfect cube, we need to multiply by a number that will make every exponent in the prime factorization into some multiple of 3. So the smallest thing we can multiply by is 2^2 * 3^1 * 5^1 = 60, since that will give us 2^3 * 3^3 * ...”
March 17, 2019
Ian Stewart posted a reply to What is the remainder when the positive integer \(n\) is in the Data Sufficiency forum
“If you know remainder arithmetic ("modular arithmetic"), this is a three-second question, because if you''re dividing by k, then "k+1" is the same as "1", so (k+1)^3 is the same as 1^3, and our remainder is 1 using Statement 1. But that won''t make any sense to most ...”
March 17, 2019
Ian Stewart posted a reply to If a light bulb is selected at random from a shipment, what in the Data Sufficiency forum
“When you''re only selecting one thing from a group, a probability is just a ratio. If you''re asked, say, "if you pick a random student from a class, what is the probability you pick a woman?", that is the same question as "what fraction of the students are women?" So the ...”
March 17, 2019
Ian Stewart posted a reply to The next number in a certain sequence is defined by in the Data Sufficiency forum
“If our sequence contains positive values, and if we''re multiplying by some positive constant (different from one) to produce each subsequent term, the sequence is either constantly increasing (if the constant is greater than 1) or constantly decreasing. (if the constant is less than 1). Either ...”
March 17, 2019
Ian Stewart posted a reply to If \(xyz < 0\), is \(x < 0\)? in the Data Sufficiency forum
“If xyz < 0, then at least one of x, y or z must be negative. Notice that means that the smallest of the three numbers is certainly negative, because negative numbers are always smaller than positive numbers. Statement 1 tells us x < y, but maybe they''re both positive and z is negative. ...”
March 17, 2019
Ian Stewart posted a reply to \(n\) is an integer greater than or equal to \(0\). in the Data Sufficiency forum
“t_0 = 3 t_1 = 3 + 1 t_2 = 3 + 1 + 2 t_3 = 3 + 1 +2 + 3 t_4 = 3 + 1 + 2 + 3 + 4 and so on, so t_n is just equal to 3 plus the sum of the first n positive integers. The sum of the first n positive integers is just (n)(n+1)/2 (it''s the number of terms, n, times the average term, which, since ...”
March 17, 2019
GMATGuruNY posted a reply to To fill an order, a manufacturer had to produce 1000 tools in the Data Sufficiency forum
“Prompt: Total production = 1000n Statement 1: Total production for the first 5 days = 5*600 = 3000 Statement 2: Total production for the last 4 days = 4*1500 = 6000 Case 1: n=9, with no days between the first 5 days and the last 4 days Total production = 1000n = 1000*9 = 9000 Total ...”
March 17, 2019
GMATGuruNY posted a reply to What is the sum of all values of that satisfy the equation 4 in the Problem Solving forum
“For any quadratic in the form x² + bx + c = 0: Product of the roots = c Sum of the roots = -b Given equation: 4x² + 16 = 32x 4x² - 32x + 16 = 0 x² - 8x + 4 = 0 In the resulting quadratic, b=-8. Thus: Sum of the roots = -(-8) = 8. The correct answer is E.”
March 17, 2019
GMATGuruNY posted a reply to Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} in the Problem Solving forum
“One approach: Show that four of the five answers do NOT have to be true. P--> a=1, b=2, c=3, d=5, e=6, f=7, g=4 Range = 7-1 = 6, median = 4, mean = (1+2+3+5+6+7+4)/7 = 28/7 Q --> a=1, b=2, c=3, d=5, e=6, f=7 Range = 7-1 = 6, median = (3+5)/2 = 4, mean = (1+2+3+5+6+7)/6 = 24/6 = 4 ...”
March 17, 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
GMATGuruNY posted a reply to If n is a positive integer and r is the remainder when in the Data Sufficiency forum
“What is the remainder when (n+1)(n-1) is divided by 8? Statement 1: Since n is odd, both n-1 and n+1 are EVEN, implying that (n-1)(n+1) = the product of two consecutive even integers. Given any two consecutive even integers, one will be a multiple of 4, while the other will be an even ...”
March 16, 2019
GMATGuruNY posted a reply to The sum of the weekly salaries of 5 employees is $3,250. If in the Problem Solving forum
“Since each salary increases by 10%, the sum increases by 10%. 10% of 3250 = 325. Average increase per employee = (total increase)/(number of employees) = 325/5 = 65. The correct answer is E.”
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
Ian Stewart posted a reply to Two cyclists, A and B, are 145 miles apart on a straight roa in the Problem Solving forum
“In the first half hour, A covers 10 miles. So at 2pm, the cyclists are 135 miles apart. Together they will cover this distance in 3 hours, since they meet at 5pm. Since A covers 60 miles in that time, B must cover the rest, or 75 miles, and so B''s speed must be 25 mph.”
March 15, 2019
Ian Stewart posted a reply to The number \(A\) can be expressed as \(p*q\) where \(p\) and in the Data Sufficiency forum
“p and q almost always represent prime numbers in math, so I don''t like their choice of letters here. Statement 1 tells us p is divisible by 8, but not by 16. So for pq to be divisible by 16, we need q to be even, something we don''t know, so Statement 1 is not sufficient alone. Statement 2 gives a ...”
March 15, 2019
GMATGuruNY posted a reply to A rectangle has sides x and y and diagonal z. What is the pe in the Data Sufficiency forum
“Always look for special triangles such as 3-4-5 and 5-12-13. Statement 2: Case 1: https://i.postimg.cc/V0JX8Hqv/rectangle-with-x-y-and-z-1.png Case 2: https://i.postimg.cc/DWCWwPyX/rectangle-with-x-y-and-z-2.png Since each case will yield a different perimeter, INSUFFICIENT. Statement ...”
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
GMATGuruNY posted a reply to combinations in the Problem Solving forum
“The portion in red is incorrect: it should be not 4C1 but 2C1. If we select two upper case letters from two sets of twins, we must then select one lower case letter from the OTHER TWO SETS OF TWINS, yielding only two options for the lower case letter. For example: If we select A and B for the two ...”
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
GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum
“Good catch. In my solution, the lone exception (N=29) is now noted.”
March 14, 2019
Ian Stewart posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum
“The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don''t get a digit sum of ...”
March 14, 2019
GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum
“Statement 1: Any integer whose digits sum to a multiple of 3 must itself be a multiple of 3. Since N has a digit sum of 11, N+1 must have a digit sum of 12. One exception: If N=29, then N+1 = 30, which has a digit sum of 3. Since the digit sum of N+1 must be a multiple of 3 -- either 12 or 3 -- ...”
March 14, 2019
Ian Stewart posted a reply to A rectangle has sides x and y and diagonal z. What is the pe in the Data Sufficiency forum
“Statement 1 is not sufficient, since the sides could be anything. Statement 2 also isn''t sufficient, because you''ll have different perimeters when, say, the quadrilateral is a square and when it isn''t. Using both statements, squaring the equation in statement 1, we learn x^2 + y^2 - 2xy = ...”
March 14, 2019
Ian Stewart posted a reply to Are 40% of the employees attending the annual company picnic in the Data Sufficiency forum
“The wording of the question is strange (is it asking if exactly 40% are men, or at least 40%?) but regardless, with no information about how many men or women work at the company, the question clearly can''t be answered even using both statements. If equal numbers of men and women work for the ...”
March 14, 2019
GMATGuruNY posted a reply to If √x+√y=7 and √x-√y=5, what is the value of xy? in the Problem Solving forum
“Adding the two equations, we get: 2√x = 12 √x = 6 x = 36 Substituting √x = 6 into √x+√y=7, we get: 6 + √y = 7 √y = 1 y = 1 Thus: xy = 36*1 = 36 The correct answer is C.”
March 14, 2019
GMATGuruNY posted a reply to If f(x)=ax^2+bx+c, where a, b and c are integers, is b=0? in the Data Sufficiency forum
“Statement 1: Since (49, 0) and (-49, 0) are both solutions, the quadratic must be as follows: f(x) = (x-49)(x+49) = x² - 49² In the resulting quadratic, b=0. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: If x-49 is a factor of the equation, then f(49) = 0. Case ...”
March 14, 2019
GMATGuruNY posted a reply to Ashley and Vinnie work on a sales staff with 8 other in the Problem Solving forum
“From the 10 people, 5 will be selected. Thus, P(Ashley is selected) = 5/10. From the 9 remaining people, 4 will be selected. Thus, P(Vinnie is selected) = 4/9. To combine these probabilities, we multiply: 5/10 * 4/9 = 2/9. The correct answer is C. Similar problem: ...”
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
GMATGuruNY posted a reply to A cosmetics company would like to market a six-item gift in the Problem Solving forum
“From 10 items, the number of ways to choose a bundle of 6 = 10C6 = (10*9*8*7*6*5)/(6*5*4*3*2*1) = 210. Subtracting the 49 bundles already eliminated from consideration, we get: 210-49 = 161. The correct answer is B.”
March 13, 2019
GMATGuruNY posted a reply to Set M is composed of the positive even integers up to 100. in the Problem Solving forum
“For any EVENLY SPACED SET: Count = (biggest - smallest)/(increment) + 1. Average = (biggest + smallest)/2. Sum = (count)(average). The INCREMENT is the difference between successive values. Even integers between 2 and 100, inclusive: Here, the integers are EVEN, so the increment = 2. Count ...”
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
GMATGuruNY posted a reply to A set of 51 different integers has a median of 30 and a in the Problem Solving forum
“Range = biggest - smallest Smallest = biggest - range Since the range = 60, we get: Smallest = biggest - 60 To minimize the smallest integer, we must minimize the biggest integer. Since the median of the 51 distinct integers = 30, there must be 25 integers above 30, with the other 25 ...”
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
GMATGuruNY posted a reply to What is the sum of the integers from 1 to 999, inclusive? A in the Problem Solving forum
“For any set of consecutive integers: Count = biggest - smallest + 1. Average = (biggest + smallest)/2. Sum = (count)(average). In the set above: Count = 999 - 1 + 1 = 999. Average = (999 + 1)/2 = 500. Sum = (999)(500) = (1000-1)(500) = 500000-500 = 499500. The correct answer is B.”
March 13, 2019
GMATGuruNY posted a reply to Peter and Tom shared the driving on a certain trip. If Peter in the Problem Solving forum
“Let the time for each driver = 1 hour. Let the total distance = 5 miles, implying that Peter''s distance = (2/5)(5) = 2 miles and that Tom''s distance = 5-2 = 3 miles. Since Peter drives 2 miles in 1 hour, Peter''s rate = 2 mph. Since Tom drives 3 miles in 1 hour, Tom''s rate = 3 mph. Thus: ...”
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
GMATGuruNY posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum
“To form a diagonal, we must choose 2 vertices. But any pair of vertices that forms a side of the polygon cannot serve to form a diagonal. Thus: Number of diagonals = (number of ways to choose 2 vertices) - (number of sides of the polygon) When the prompt includes the phrase which of the ...”
March 12, 2019
GMATGuruNY posted a reply to Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs a in the Problem Solving forum
“To count circular arrangements: 1. Place someone in the circle 2. Count the number of ways to arrange the REMAINING people Once Alice has been placed in the circle: Number of options for Bob = 1. (Must be in the seat opposite Alice) Number of options for Cindy = 4. (Any of the 4 remaining ...”
March 12, 2019
GMATGuruNY posted a reply to If x and y are positive integers, x/y=? in the Data Sufficiency forum
“Statement 1: Case 1: x=2 and y=1, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 2/1 = 2. Case 2: x=1 and y=2, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 1/2 = 1/2. Since x/y can be different values, INSUFFICIENT. Statement 2: Here, x=2 ...”
March 12, 2019
GMATGuruNY posted a reply to Roman City in the Critical Reasoning forum
“E: mosaic designs with which artisans who lived in various parts of the Roman Empire were familiar. Here, the two blue portions constitute an adjective serving to modify designs. Question: What KIND of designs? Answer: Designs WITH WHICH ARTISANS WERE FAMILIAR. Put another way: Artisans were ...”
March 11, 2019
GMATGuruNY posted a reply to Carmen currently works 30 hours per week at her part-time jo in the Data Sufficiency forum
“Rate and time have a RECIPROCAL relationship. If the hourly rate DOUBLES, then the same income will be yielded in 1/2 the total time. Statement 1: Actual hourly rate = 225/30 = $7.50, implying that an additional $1.50 per hour will increase the hourly rate to $9. (increased hourly ...”
March 11, 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
GMATGuruNY posted a reply to schistosomiasis and malaria. in the Critical Reasoning forum
“M --> more than 50% of all disease cases over the past 5 years S --> 40% of all disease cases 5 years ago, 30% of all disease cases now For each answer choice: Try to devise a case that aligns with the information in the passage but CONTRADICTS the answer choice, thus proving that the ...”
March 9, 2019
Ian Stewart posted a reply to A certain game board is in the shape of a non-convex polygon in the Data Sufficiency forum
“Statement 1 is always true, so is useless, while Statement 2 obviously gives you one equation in one unknown, so is sufficient. But test takers don''t need to know anything about ''exterior angles'' for the GMAT, nor what a ''non-convex polygon'' is, not to mention that Statement 2 is problematic ...”
March 9, 2019
GMATGuruNY posted a reply to Verbal Review 18 : Kudzu, an Asian vine in the Sentence Correction forum
“Generally, COMMA + SINCE after a clause serves to express a CAUSAL relationship. An OA in GMATPrep: Prospecting for gold was a relatively easy task, since erosion put gold literally within reach of anybody with a pan. Here, the clause in blue serves to express what CAUSED prospecting to be a ...”
March 9, 2019
GMATGuruNY posted a reply to If p is a positive integer, is 2p + 1 prime? in the Data Sufficiency forum
“Statements combined: Case 1: p=11 --> p is prime, but its units digits is not prime In this case, 2p+1 = 2*11 + 1 = 23. Since 23 is prime, the answer to the question stem is YES. Case 2: p=19 --> p is prime, but its units digit is not prime In this case, 2p+1 = 2*19 + 1 = 39. Since 39 ...”
March 9, 2019
GMATGuruNY posted a reply to If a certain reel of film runs at 5/6 of a frame per second, in the Problem Solving forum
“2580 frames * (1 second)/(5/6 frame per second) * (1 minute)/(60 seconds) = 2580/50 = a little over 50 minutes. The correct answer is B.”
March 9, 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
GMATGuruNY posted a reply to When positive integer x is divided by positive interger y, in the Problem Solving forum
“When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL. There is a relationship between the two representations: Remainder/Divisor = Decimal. When 5 is divided by 2: Remainder representation: 5/2 = 2 R1 Decimal ...”
March 8, 2019
GMATGuruNY posted a reply to The R students in a class agree to contribute equally to buy in the Problem Solving forum
“Let y=$10 and R=10 students, with the result that the original share per student = ($10)/(10 students) = $1. Let x=9, implying that the number of students decreases by 9 to 1. New share per student = ($10)/(1 student) = $10. Increase in share per student = 10-1 = $9. The correct answer must ...”
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
Ian Stewart posted a reply to In the figure shown, point O is the center of the circle and in the Data Sufficiency forum
“This is exactly identical to a GMATPrep question: https://gmatclub.com/forum/in-the-figure-shown-point-o-is-the-center-of-the-semicircle-89662.html”
March 7, 2019
GMATGuruNY posted a reply to Is the average (arithmetic mean) of x, y, and z equal to the in the Data Sufficiency forum
“Statement 1: In other words, y is HALFWAY BETWEEN x and z, implying that x, y and z are EVENLY SPACED. For any evenly spaced set, the average = the median. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: x+z = 2y (x+z)/2 = y Implication: y is the average of x and z ...”
March 7, 2019
GMATGuruNY posted a reply to What is the remainder when -12 is divided by -5? in the Problem Solving forum
“This problem is not relevant to the GMAT. On the GMAT, problems involving remainders are constrained to POSITIVE INTEGERS. From the Math Review in the OG: If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r ...”
March 7, 2019
Ian Stewart posted a reply to At a particular moment, a restaurant has x biscuits and y pa in the Data Sufficiency forum
“It makes no sense to ask a DS question in this way. If y is a "number of patrons" in a real GMAT DS question, then y stands for a single unknown value; it doesn''t stand for a variable. You can''t ask "how many values of y are possible?" in DS, because it''s not clear what ...”
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
Ian Stewart posted a reply to Each of the items in a box is either a ball or a cube and ea in the Problem Solving forum
“The above solution isn''t right. If we have 100 objects, we have 72 cubes. If 54 of these are blue, the rest, or 18, are red. The question asks "What percent of the cubes are red?", and we have 18 red cubes and 72 cubes in total, so the answer is 18/72 = 1/4 = 25%.”
March 6, 2019
Ian Stewart posted a reply to What is the sum of all of the integers in the chart above? in the Problem Solving forum
“In each column, if we list the numbers in increasing order, we get an equally spaced list with a multiple of 100 in the middle. So, for example, the second column contains the numbers: -204, -202, -200, -198, -196 The sum of an equally spaced list is just equal to the average (which, in an ...”
March 6, 2019
Ian Stewart posted a reply to Eight friends go to watch a movie but only 5 tickets were in the Problem Solving forum
“I don''t like the wording of the question, because it''s not altogether clear if order should matter. But that''s the intention, so we have 8 choices for which person goes in the first seat, 7 for the next seat, and so on, and multiplying our choices gives the answer of (8)(7)(6)(5)(4).”
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
Ian Stewart posted a reply to Among the members of the Malmo family, there are three times in the Problem Solving forum
“It''s a pure ratio/percent problem, so we can freely make up a number, and since we''re asked for a percent in the end, I''d just use 100. Then we have: 50 have blue eyes, of whom: 40 have blue eyes and no glasses 10 have blue eyes and glasses We also know that the ratio of ...”
March 5, 2019
Ian Stewart posted a reply to If j and k are positive integers where k > j, what is the in the Data Sufficiency forum
“Statement 1 says, in words, "k is 5 greater than some multiple of of j". If j > 5, then that''s just another way of saying "the remainder is 5 when we divide k by j". But we don''t know if j > 5, using only Statement 1. If j=2, say, then it''s impossible for the remainder ...”
March 5, 2019
GMATGuruNY posted a reply to A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum
“Given that the area and the answer choices are all integers, the triangle is probably a Pythagorean Triple. The only Pythagorean Triple with an area of 30 is 5-12-13. In the given equation, test c=5, with the result that c+7 = 12: x/5 + y/12 - 1 = 0 If x=0, then y=12, implying a y-intercept ...”
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
GMATGuruNY posted a reply to Joey works at a clothing store and receives an employee in the Problem Solving forum
“Since the discount = 10% = 1/10, and the resulting discount price is an integer value, the regular price must be a dollar value that is a multiple of 10. The correct answer is E.”
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
GMATGuruNY posted a reply to When 32 is divided by k, the remainder is k-3. What is the in the Data Sufficiency forum
“Dividing 32 by k leaves a remainder of k-3. In other words, 32 is equal to k-3 more than a multiple of k: 32 = ak + (k-3), where a is a nonnegative integer and k is an integer such that k≥3. Simplifying 32 = ak + (k-3), we get: 35 = ak + k 35 = k(a+1) The resulting equation implies that ...”
March 5, 2019
GMATGuruNY posted a reply to If x and y are positive integers and (x-y)^2+y^2=25, which o in the Problem Solving forum
“Identify two perfect squares that sum to 25: 1, 4, 9, 16... The two values in blue sum to 25. If y=3 and x=7, then (x-y)² = (7-3)² = 16 and y² = 9, with the result that (x-y)² + y² = 25. The correct answer is B.”
March 5, 2019
Ian Stewart posted a reply to In how many ways can 16 different gits be divided among four in the Problem Solving forum
“If you know that in any counting situation, when the order of k things doesn''t matter, you can first pretend order does matter and then divide by k!, then you can just: imagine putting all 16 gifts in a row, which you can do in 16! ways. Give the first four gifts to the oldest child, the next four ...”
March 4, 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
Ian Stewart posted a reply to When 900 is divided by positive integer d, the remainder is in the Data Sufficiency forum
“Each Statement is clearly insufficient alone, because using only one statement, we know almost nothing about one of the two unknowns in the inequality in the question. Using Statement 1, we know when 900 is divided by d, the remainder is 1. That means that 900 is exactly 1 larger than some ...”
March 3, 2019
Ian Stewart posted a reply to In five football games thus far this season, Barry has run f in the Problem Solving forum
“The wording here is problematic for a few reasons - it needs to mention that yard totals must be integers (that''s not going to be intuitive or obvious to someone who doesn''t follow football), it should say ''yards per game'', and it should certainly not ask what Barry needs to do to "keep his ...”
March 3, 2019
Ian Stewart posted a reply to The positive two-digit integers x and y have the same digits in the Problem Solving forum
“If AB is a two digit number, where A is the tens digit and B the units digit, then the number is equal to 10A + B. Here we are adding AB and BA, which is the same as adding 10A+B and 10B + A. Adding those we get 11A + 11B, which clearly has 11 as a factor.”
March 3, 2019
GMATGuruNY posted a reply to OG Before 1988, insurance companies in California in the Sentence Correction forum
“Generally, COMMA + VERBing serves to modify the nearest preceding action and the agent of this action. Given this rule, I received a PM requesting that I justify the usage of COMMA + needing in the OA: Insurance companies in California were free to charge whatever rates the market would bear, ...”
March 3, 2019
Ian Stewart posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum
“Anyone interested in my GMAT math books or problem sets can contact me at the email address below.”
March 2, 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
Ian Stewart posted a reply to If y is a positive integer, is y prime? in the Data Sufficiency forum
“This is a near-exact replica of an official question. Statement 1 is clearly not sufficient, because there is an infinite number of primes. I think Statement 2 is supposed to read: 11! - 12 < y < 11! - 2 That''s also not sufficient, because each number in that interval has an obvious ...”
March 2, 2019
GMATGuruNY posted a reply to In a certain school, there are 160 boys and 240 girls. If 15 in the Problem Solving forum
“Left-handed boys = 15% of 160 = 24. Left-handed girls = 25% of 240 = 60. (total left-handed)/(total students) = (24+60)/(160+240) = 84/400 = 21/100 = 21%. The correct answer is C.”
March 2, 2019