# meenanke

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, ...”
Today
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 ...”
Today
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 ...”
Today
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 ...”
Today
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 ...”
Yesterday
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”
Yesterday
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”
Yesterday
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
fskilnik@GMATH posted a reply to If 5 is approximately equal to 2^(2.322), which of the follo in the Problem Solving forum
“$${2^{2.322}} \cong 5\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{2^{2.322}}} \right)^{0.5}} = {5^{0.5}}\left( * \right)$$ $${{{2^{ - 5}} \cdot \root 3 \of {{{10}^2}} } \over {\root 6 \of {10} \cdot {2^x}}} = 1\,\,\,\, \Rightarrow \,\,\,{{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{{2^x}} ...” March 18, 2019 fskilnik@GMATH posted a reply to There are many boxes in a certain room, and each box has a l in the Problem Solving forum “$$4 \cdot 1 + 4 \cdot 2 + \ldots + 4 \cdot N = 612? = N\,\,\,\,\left( {N \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\left( * \right)612 = 4(1 + 2 + \ldots + N)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.Seq}}} \,\,\,4\leftGMATH method. Regards, Fabio.”
March 18, 2019
fskilnik@GMATH posted a reply to If A>B are two odd numbers, how many even numbers are the in the Problem Solving forum
“$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\leftSecond Approach ("the technical way"):$$? = \# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,I = \leftGMATH method. Regards, Fabio.”
March 18, 2019
fskilnik@GMATH posted a reply to If A>B are two odd numbers, how many even numbers are the in the Problem Solving forum
“$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\leftFirst Approach ("the smart way"):$${\rm{Take}}\,\,\left( {B,A} \right) = \left( {1,5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Target}} = 2\,\,\,\,\,\leftGMATH method. Regards, Fabio.”
March 18, 2019
fskilnik@GMATH posted a reply to If f is a function defined for every positive integer x in s in the Problem Solving forum
“$${x^2} \cdot f\left( x \right) = {2^{8 - x}}\,\,\,\,\left( * \right)$$ $$? = 100 \cdot f\left( 5 \right)$$ $$x = 5\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,25 \cdot f\left( 5 \right) = {2^3}\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,4} \,\,\,\,? = 4 \cdot {2^3} = ...” March 18, 2019 fskilnik@GMATH posted a new topic called There are many boxes in a certain room, and each box has a l in the Problem Solving forum “GMATH practice exercise (Quant Class 17) There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels ...” March 17, 2019 fskilnik@GMATH posted a new topic called If A>B are two odd numbers, how many even numbers are there in the Problem Solving forum “GMATH practice exercise (Quant Class 16) If A>B are two odd numbers, how many even numbers are there between them? (A) (A+B)/2 (B) A-B+1 (C) A-B (D) A-B-1 (E) (A-B)/2 Answer: _____(E)__ ” March 17, 2019 Ian Stewart posted a reply to A carpenter worked alone for 1 day on a job that would take in the Problem Solving forum “Once the first day is done, 6/7 of the job is left. We then know that the two workers together do 6/7 of a job in 4 days. So now we know these two things: Carpenter A does 1 job in 7 days Carpenters A+B together do 6/7 jobs in 4 days We can now get the same time for both: A does 4 jobs ...” March 17, 2019 Ian Stewart posted a reply to What is the smallest positive integer $$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$$. in the Data Sufficiency forum “t_0 = 3 t_1 = 3 + 1 t_2 = 3 + 1 + 2 t_3 = 3 + 1 +2 + 3 t_4 = 3 + 1 + 2 + 3 + 4 and so on, so t_n is just equal to 3 plus the sum of the first n positive integers. The sum of the first n positive integers is just (n)(n+1)/2 (it''s the number of terms, n, times the average term, which, since ...” March 17, 2019 fskilnik@GMATH posted a new topic called If f is a function defined for every positive integer x in s in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/SsDKwW9r/17-Mar19-6y.gif Answer: _____(C)__” March 17, 2019 fskilnik@GMATH posted a new topic called If 5 is approximately equal to 2^(2.322), which of the follo in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.postimg.cc/cJzYVGNC/17-Mar19-3g.gif Answer: _____(B)___” March 17, 2019 fskilnik@GMATH posted a reply to If quadrilaterals ABCD and ADEF have the same areas, is AF&a in the Data Sufficiency forum “https://i.postimg.cc/fTD6f9kR/15-Mar19-10q.gif$${S_{{\mathop{\rm ABCD}\nolimits} }} = {S_{{\rm{ADEF}}}} = {S_{{\rm{ADEG}}}} + {S_{{\rm{AGF}}}}\,\,\,\,\,\left( * \right)AF\,\,\mathop > \limits^? \,\,28\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{image}}\,\,{\rm{left}}:\,\,\left( ...”
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 fskilnik@GMATH posted a new topic called If quadrilaterals ABCD and ADEF have the same areas, is AF>2 in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.postimg.cc/hGP6RWVW/15-Mar19-3w.gif If quadrilaterals ABCD and ADEF have the same areas, is AF > 28 ? (1) EF = 10 (2) CE = 24 Answer: ______(C)__ ” 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 fskilnik@GMATH posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “Thank you both (Mitch and Ian) for your nice contributions! $$N = \left\langle {AB} \right\rangle$$ $$N + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$ $$\left( 1 \right)\,\,A + B = 11\,\,\,\,\left\{ \matrix{ \,B\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle ...” March 14, 2019 fskilnik@GMATH posted a reply to What is the selling price (in dollars) of the HK11B-connecto in the Data Sufficiency forum “$$s,c\,\,\, \to \,\,\,\,\leftGMATH method. Regards, Fabio.” 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 fskilnik@GMATH posted a new topic called If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 16) If N is a positive two-digit integer, is N+1 prime? (1) The sum of the digits of N is equal to 11. (2) N-1 is divisible by 7. Answer: _____(A)__” March 14, 2019 fskilnik@GMATH posted a new topic called What is the selling price (in dollars) of the HK11B-connecto in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) What is the selling price (in dollars) of the HK11B-connector (a specific electronic widget) in Mrs. Tao´s store? (1) In Mrs. Tao´s store, the difference between the selling price of the HK11B-connector and the cost of this electronic widget is 500 ...” 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 fskilnik@GMATH posted a reply to If c is a nonzero constant such that x*f(x) = c, variables x in the Problem Solving forum “https://i.postimg.cc/258f4wYr/13-Mar19-8w.gif $$? = c = {1 \over 2} \cdot b\,\,\,\,\,\,\leftGMATH method. Regards, Fabio.” March 13, 2019 fskilnik@GMATH posted a reply to An airplane leaves city A to make a connection in city C, be in the Problem Solving forum “https://i.postimg.cc/fbknkfmF/13-Mar19-4g.gif$$?\,\,\, \cong \,\,\,AC + CB\,\,\,\,\leftGMATH method. Regards, Fabio.” March 13, 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 fskilnik@GMATH posted a reply to The number of candidates rejected in a certain admission pro in the Problem Solving forum “$$?\,\,\,:\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,\,\left( {{\rm{possible}}\,\,{\rm{value}}} \right)$$ $$\left\{ \matrix{ \,{\rm{accepted}} = k \hfill \cr \,{\rm{rejected}} = 5k \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6k\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm ...” 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 fskilnik@GMATH posted a new topic called If c is a nonzero constant such that x*f(x) = c, variables x in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.postimg.cc/8cxcjYfy/13-Mar19-7z.gif If c is a nonzero constant such that x*f(x) = c, variables x and y=f(x) are said to be inversely proportional. If the dotted curve shown above, defined by the points (x,y) where x>0 and y=f(x), represents ...” 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 fskilnik@GMATH posted a new topic called An airplane leaves city A to make a connection in city C, be in the Problem Solving forum “GMATH practice exercise (Quant Class 2) https://i.postimg.cc/J7NbScJb/13-Mar19-3w.gif An airplane leaves city A to make a connection in city C, before going on to city B (as shown in the map). If the map scale is 1cm=100km, which of the following is closest to the minimum possible distance ...” 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 fskilnik@GMATH posted a new topic called The number of candidates rejected in a certain admission pro in the Problem Solving forum “GMATH practice exercise (Quant Class 6) The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted. Which of the following could be the total number of candidates that applied for this admission process? (A) 726 (B) 727 (C) ...” 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 fskilnik@GMATH posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum “Let´s connect Mitch´s nice argument with mine (above):$$d = C\left( {N,2} \right) - N = {{N!} \over {2!\left( {N - 2} \right)!}} - N = {{N\left( {N - 1} \right)} \over 2} - {{2N} \over 2} = {{N\left( {N - 3} \right)} \over 2}$$Regards, Fabio.” March 12, 2019 fskilnik@GMATH posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum “$$?\,\,\,:\,\,\,\# \,d\,\,\underline {{\rm{could}}\,\,{\rm{be}}} \,\,\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} \,\,\left( * \right)\,,\,\,N{\rm{ - polygon}}} \right)d\,\, \to \,\,\,\left\{ \matrix{ \,{\rm{each}}\,\,{\rm{vertex}}\,\,{\rm{with}}\,\,\left( {{\rm{not}}\,\,{\rm{itself}}} ...” March 12, 2019 fskilnik@GMATH posted a reply to Claudio wants to be well prepared for a long marathon that w in the Problem Solving forum “$$?\,\,\,:\,\,\,\min \,N\,\,{\rm{for}}\,\,{\rm{sum}}\,\,\, \ge \,\,\,1800\,$$ $$\left. \matrix{ {a_1} = 15 \hfill \cr {a_2} = 15 + 1 \cdot {1 \over 2} \hfill \cr {a_3} = 15 + 2 \cdot {1 \over 2} \hfill \cr \vdots \hfill \cr {a_N} = 15 + \left( {N - 1} \right) \cdot {1 \over ...” March 12, 2019 fskilnik@GMATH posted a reply to If c is a constant such that the system of equations given a in the Problem Solving forum “$$?\,\,\,:\,\,\,c\,\,\,{\rm{for}}\,\,{\rm{unique}}\,\,{\rm{solution}}\,\,\left( {x,y} \right)c = 0\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x = 1 \hfill \cr \, - 4y = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {1,0} ...” March 12, 2019 fskilnik@GMATH posted a new topic called If c is a constant such that the system of equations given a in the Problem Solving forum “GMATH practice exercise (Quant Class 10) https://i.postimg.cc/qB8ZZCpW/12-Mar19-3w.gif Answer: _____(E)__” March 12, 2019 fskilnik@GMATH posted a new topic called Claudio wants to be well prepared for a long marathon that w in the Problem Solving forum “GMATH practice exercise (Quant Class 17) Claudio wants to be well prepared for a long marathon that will occur in the near future. His running coach has decided that the training sessions must be done once every two days, starting with a 15-kilometer distance route, and adding exactly 500 ...” March 12, 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 fskilnik@GMATH posted a reply to If x>0, what is the sum of the roots of the equation x^sq in the Problem Solving forum “$$x > 0\,\,,\,\,\,\,{x^{\sqrt x }} = {x^2}\,\,\,\left( * \right)$$ $$?\,\,:\,\,{\rm{sum}}\,\,{\rm{of}}\,\,{\rm{roots}}$$ $$x = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{inspection}}} \,\,\,\,\left\{ \matrix{ \,\,{x^{\sqrt x }} = {1^{\sqrt 1 }} = 1 \hfill \cr \,\,{x^2} = {1^2} = 1 ...” March 11, 2019 fskilnik@GMATH posted a reply to What is the ordinate (y-coordinate) of point C? in the Data Sufficiency forum “$$? = {y_C}$$https://i.postimg.cc/sxr9WGzd/11-Mar19-7v.gif$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,OD = 2\sqrt 2 \hfill \cr \Delta AOB\,\,{\rm{isosceles}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,\Delta ODB\,\,{\rm{isosceles}} \hfill \cr ...” March 11, 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 fskilnik@GMATH posted a new topic called If x>0, what is the sum of the roots of the equation x^sqrt( in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.postimg.cc/T3Jw2y75/11-Mar19-8k.gif Answer: _____(E)__” March 11, 2019 fskilnik@GMATH posted a new topic called What is the ordinate (y-coordinate) of point C? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 20) https://i.postimg.cc/pXvnJtFv/11-Mar19-6j.gif Answer: _____(C)__” March 11, 2019 fskilnik@GMATH posted a reply to Is (x^2-7x+12)(x^2-5x-14) > 0 ? in the Data Sufficiency forum “$$\left( {x - 3} \right)\left( {x - 4} \right)\left( {x + 2} \right)\left( {x - 7} \right)\,\,\mathop > \limits^? \,\,0$$ $$\left( 1 \right)\,\,x > 0\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 3\,\,\,\, \Rightarrow \,\,\,\left( {x - 3} \right)\left( {x - 4} \right)\left( {x + 2} ...” March 10, 2019 fskilnik@GMATH posted a reply to If (x-1)/(x-3)>(x-2)/(x-4) is equivalent to a<x<b, in the Problem Solving forum “https://i.postimg.cc/QMJ6zv72/10-Mar19-8p.gif Regards, Fabio. ” March 10, 2019 fskilnik@GMATH posted a reply to If (x-1)/(x-3)>(x-2)/(x-4) is equivalent to a<x<b, in the Problem Solving forum “https://i.postimg.cc/qq5DLnKg/10-Mar19-7w.gif The correct answer is (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” March 10, 2019 fskilnik@GMATH posted a reply to If F is a function defined in the positive integers, such th in the Data Sufficiency forum “$$F\left( k \right) \ge 1\,\,{\mathop{\rm int}} \,\,\,\,{\rm{for}}\,\,{\rm{each}}\,\,\,k \ge 1\,\,\,\,\left( * \right)? = F\left( 8 \right)\left( 1 \right)\,\,F\left( {n + 1} \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge ...” March 10, 2019 fskilnik@GMATH posted a new topic called Is (x^2-7x+12)(x^2-5x-14) > 0 ? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) Is (x^2-7x+12)(x^2-5x-14) > 0 ? (1) x > 0 (2) 3 < |x| < 4 Answer: _____(B)__” March 10, 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 fskilnik@GMATH posted a new topic called If (x-1)/(x-3)>(x-2)/(x-4), then a<x<b, where: in the Problem Solving forum “GMATH practice exercise (Quant Class 11) https://i.postimg.cc/ZKH5VMYt/10-Mar19-6w.gif Answer: _____(D)__” March 10, 2019 fskilnik@GMATH posted a new topic called If F is a function defined in the positive integers, such th in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)? (1) F(n+1) = (n+1)*F(n), for every positive integer n. (2) F(1)*F(1) = F(1) Answer: _____(C)__” 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 fskilnik@GMATH posted a reply to If 0.845 is an approximate solution for the equation 10^x = in the Problem Solving forum “$${10^{0.845}} \cong 7$$ $${7^{x + 2}} = 70$$ $$?\,\, \cong x\,\,\,\,\,\,$$ $${7^{x + 2}} = 7 \cdot 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{7^{x + 1}} = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{7^{x + 1}}} \right)^{0.845}} = {10^{0.845}}\,\, \cong \,\,\,7$$ $${7^{0.845\left( {x + 1} \right)}} ...” March 8, 2019 fskilnik@GMATH posted a reply to If the raining season in Jerusalem begins, Dora estimates a in the Problem Solving forum “$$? = P\left( {{\rm{Dora}}\,\,{\rm{travels}}} \right)P\left( {{\rm{season}}\,\,{\rm{raining}}} \right) = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,P\left( {{\rm{not}}\,\,{\rm{season}}\,\,{\rm{raining}}} \right) = 30\% 20\% \,\,\mathop \to \limits^{\, + \,250\% } \,\,\,\underbrace {60\% + ...” March 8, 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 fskilnik@GMATH posted a new topic called If 0.845 is an approximate solution for the equation 10^x = in the Problem Solving forum “GMATH practice exercise (Quant Class 3) If 0.845 is an approximate solution for the equation 10^x = 7, which of the following fractions is closest to the solution of 7^(x+2) = 70? (A) 29/211 (B) 19/107 (C) 31/169 (D) 43/211 (E) 53/211 Answer: _____(C)__” March 8, 2019 fskilnik@GMATH posted a new topic called If the raining season in Jerusalem begins, Dora estimates a in the Problem Solving forum “GMATH practice exercise (Quant Class 19) If the raining season in Jerusalem begins, Dora estimates a 20% probability of traveling to Israel next holidays. If it doesn´t, she guesses her probability of taking this trip is 250% higher. Based on these assumptions, what are Dora´s chances of ...” March 8, 2019 fskilnik@GMATH posted a reply to What percent of the area of the rhombus ABCD is the area of in the Data Sufficiency forum “https://i.postimg.cc/RZ2d0s7n/08-Mar19-2x.gif $$? = {{{S_{{\rm{circle}}}}} \over {{S_{{\rm{rhombus}}}}}}$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ BCD = {60^ \circ } \hfill \cr ABCD\,\,{\rm{rhombus}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta ...” March 8, 2019 GMATGuruNY posted a reply to When positive integer x is divided by positive interger y, in the Problem Solving forum “When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL. There is a relationship between the two representations: Remainder/Divisor = Decimal. When 5 is divided by 2: Remainder representation: 5/2 = 2 R1 Decimal ...” March 8, 2019 GMATGuruNY posted a reply to The R students in a class agree to contribute equally to buy in the Problem Solving forum “Let y=10 and R=10 students, with the result that the original share per student = (10)/(10 students) = 1. Let x=9, implying that the number of students decreases by 9 to 1. New share per student = (10)/(1 student) = 10. Increase in share per student = 10-1 = 9. The correct answer must ...” March 8, 2019 fskilnik@GMATH posted a reply to If 0.02 < x < 0.04 and 100 < y < 250, which of t in the Problem Solving forum “$$?\,\,\,:\,\,\,\frac{{y - x}}{{xy}} = \frac{1}{x} - \frac{1}{y}\,\,\,\,\,\underline {{\text{could}}\,\,{\text{be}}} {2 \over {100}} < x < {4 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,25 = {{100} \over 4} < {1 \over x} < {{100} \over 2} = 50\,\,\,\,\left( {\rm{I}} \right)$$...” March 8, 2019 fskilnik@GMATH posted a new topic called What percent of the area of the rhombus ABCD is the area of in the Data Sufficiency forum “GMATH practice exercise (Quant Class 19) https://i.postimg.cc/Kv2v8SQL/07-Mar19-7h.gif What percent of the area of the rhombus ABCD is the area of the circle that is inscribed in it? (1) Angle BCD is equal to 60 degrees (2) AB = 4 Answer: _____(A)__ ” March 7, 2019 fskilnik@GMATH posted a reply to W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “Beautiful problem, Brent. Congrats!$$W,X,Y,Z\,\,\, \ge 1\,\,\,{\rm{different}}\,\,{\rm{ints}}\,\,\left( * \right)\left\{ \matrix{ X = ZY + W\,\,,\,\,\,W < Y\,\,\,\left( {**} \right) \hfill \cr \left( * \right)\,\,\,1 \le W < Y\,\,\, \Rightarrow \,\,\,Y \ge 2\,\,\,\left( {***} ...” March 7, 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 fskilnik@GMATH posted a reply to Little Julia created a 5-digit integer choosing 5 distinct c in the Problem Solving forum “$$?\,\, = \,\,{1 \over {\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}}}$$ $${?_{temp}}\,\,\, = \,\,\,\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}$$ $$\left\{ \matrix{ \,{\rm{3}}\,{\rm{central}}\,{\rm{digits}}\,{\rm{are}}\,\,{\rm{1,3,5}}\,\,\,\, \Rightarrow \,\,\,{{\rm{P}}_{\rm{3}}} = ...” March 7, 2019 Brent@GMATPrepNow posted a new topic called W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. What is the value of Z? 1) W = X – 4 2) W + Z = 4 Difficulty level: 650 – 700 Source: www.gmatprepnow.com” March 7, 2019 Brent@GMATPrepNow posted a reply to 60 DAY STUDY GUIDE ENQUIRY in the Ask a GMAT Prep Now representative forum “Sorry, but there are no plans to update the 60-day guide in the near future. Cheers, Brent” March 7, 2019 fskilnik@GMATH posted a reply to In the figure shown, all angles are measured in degrees. Wha in the Problem Solving forum “https://i.postimg.cc/ZR8PpLSq/07-Mar19-6r.gif$$? = k\,\,\,\leftGMATH method. Regards, Fabio.” 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 fskilnik@GMATH posted a new topic called Little Julia created a 5-digit integer choosing 5 distinct c in the Problem Solving forum “GMATH practice exercise (Quant Class 18) https://i.postimg.cc/0QtN8gvh/07-Mar19-4u.gif Little Julia created a 5-digit integer choosing 5 distinct chips, one by one, among the 7 given ones shown above. "Can you do it in such a way that the three central digits add up to 9?", asked ...” March 7, 2019 fskilnik@GMATH posted a reply to A certain Formula 1 car fuel consumption is 2.5 liters per k in the Problem Solving forum “$$?\,\,\, = \,\,\,\max \,\,{\rm{laps}}\,\,\,\left( {{\rm{between}}\,\,{\rm{pit - stops}}} \right)$$ $$3.5\,\,{\rm{km}}\,\,\,\, \leftrightarrow \,\,\,\,{\rm{1}}\,\,{\rm{lap}}\,\,\,\,\,$$ $${\rm{consumption}}\,\,:\,\,2.5\,\,{\rm{liters}}\,\,\,\, \leftrightarrow \,\,\,\,{\rm{1}}\,\,{\rm{km}}$$ ...” March 7, 2019 fskilnik@GMATH posted a new topic called In the figure shown, all angles are measured in degrees. Wha in the Problem Solving forum “GMATH practice exercise (Quant Class 1) https://i.postimg.cc/CL0hnHMc/07-Mar19-5c.gif In the figure shown, lines m and n are parallel and all angles are measured in degrees. What is the value of k? (A) 18 (B) 20 (C) 22 (D) 25 (E) 27 Answer: _____(B)__” 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 fskilnik@GMATH posted a new topic called A certain Formula 1 car fuel consumption is 2.5 liters per k in the Problem Solving forum “GMATH practice exercise (Quant Class 5) A certain Formula 1 car fuel consumption is 2.5 liters per kilometer, and the supply pump injects 11 liters of fuel per second. Every time a pit stop for refueling is needed (i.e., the fuel tank is almost empty), fuel is injected during 6.5 seconds. In a ...” 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 fskilnik@GMATH posted a reply to The figure above shows the representations of the graphs of in the Problem Solving forum “https://i.postimg.cc/QtpV8gKg/05-Mar19-5z.gif $$? = g\left( {f\left( 0 \right)} \right)$$ $$\leftGMATH method. Regards, Fabio.” March 5, 2019 Brent@GMATPrepNow posted a reply to Is xy>3? in the Data Sufficiency forum “Target question: Is xy > 3 ? Statement 1: (7^x) > 729 Since there''s no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7 Since there''s no information about x, we cannot answer the target question with ...” March 5, 2019 fskilnik@GMATH posted a reply to Karina´s mother has already bought T attraction tickets to in the Data Sufficiency forum “$$N\,\, = \,\,\,\# \,\,{\rm{friends}}? = 4N - T\left( 1 \right)\,\,T = 2N + 25\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {20,65} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,15 \hfill \cr \,{\rm{Take}}\,\,\left( {N,T} \right) = ...” March 5, 2019 fskilnik@GMATH posted a reply to A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum “Yes... 5-12-13 is an important GMAT Pythagorean Triple... $$?\,\, = \,\,\Delta \,\,{\rm{perimeter}}$$ $${S_\Delta } = 30\,\,\,\left( * \right)$$ $${x \over c} + {y \over {c + 7}} = 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x{\rm{ - intercept}} = c \hfill \cr \,y{\rm{ - ...” March 5, 2019 fskilnik@GMATH posted a reply to Is xy>3? in the Data Sufficiency forum “$$xy\,\,\mathop > \limits^? \,\,3\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\leftGMATH method. Regards, Fabio.” March 5, 2019 fskilnik@GMATH posted a new topic called Is xy>3? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) Is xy > 3 ? (1) (7^x) > 729 (2) (9^y) = 7 Answer: _____(C)__ P.S.: this IS in GMAT´s quant section scope.” March 5, 2019 fskilnik@GMATH posted a new topic called The figure above shows the representations of the graphs of in the Problem Solving forum “GMATH practice exercise (Quant Class 13) https://i.postimg.cc/VNyhqzps/05-Mar19-4q.gif The figure above shows the representations of the graphs of the functions f and g, where f(x) = 2^(-0.5x) and g(x) = ax^2+b (a and b constants). What is the value of g(f(0)) ? (A) 3 (B) 3.25 (C) ...” 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 fskilnik@GMATH posted a new topic called Karina´s mother has already bought T attraction tickets to d in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) Karina´s mother has already bought T attraction tickets to distribute to Karina´s friends for the party at the Alice-In-Wonderland amusement park. How many extra attraction tickets must Karina´s mother buy if Karina decides to give four tickets to each ...” 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 fskilnik@GMATH posted a new topic called A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum “GMATH practice exercise (Quant Class 20) A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52 Answer: _____(C)__” 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 fskilnik@GMATH posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum “Dear aflaam messih, Thank you for your kind words. We are happy to use our GMAT experience to contribute to this wonderful community. Feedbacks like yours are marvelous. They tell us we are in the right direction! See you in other posts and success in your studies! Fabio.” March 4, 2019 fskilnik@GMATH posted a reply to If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the in the Problem Solving forum “$$? = 3x + 2y + z$$ $${\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2} = - {\left( {3y - z} \right)^2}\,\,\,\,\,\left( * \right)$$ $$\left. \matrix{ {\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2}\,\,\, \ge ...” March 4, 2019 fskilnik@GMATH posted a reply to If a<b<0 are integers, what is the value of a^3-b^3? in the Data Sufficiency forum “$$? = {a^3} - {b^3}\,a < b < 0\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)\left( 1 \right)\,\,\,\left\{ \matrix{ \,\left( {a + b} \right)\left( {a - b} \right) = 65 = 1 \cdot 65 = 5 \cdot 13 \hfill \cr \,\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,a + b < a - b\,\,\, ...” March 4, 2019 fskilnik@GMATH posted a new topic called If a<b<0 are integers, what is the value of a^3-b^3? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 16) https://i.postimg.cc/rF138gcp/03-Mar19-13q.gif Answer: ____(C)__” March 4, 2019 fskilnik@GMATH posted a reply to What is the value of (2-1/3)(1+1/4)^(-1)(1+2/5)? in the Problem Solving forum “$$\,? = \left( {2 - {1 \over 3}} \right){\left( {1 + {1 \over 4}} \right)^{ - 1}}\left( {1 + {2 \over 5}} \right)\,\,$$ $$\left. \matrix{ 2 - {1 \over 3} = {{2 \cdot 3} \over 3} - {1 \over 3} = {5 \over 3} \hfill \cr 1 + {1 \over 4} = {5 \over 4}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {1 + ...” March 3, 2019 fskilnik@GMATH posted a reply to If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is: in the Problem Solving forum “$$?\,\, = \,\,{{2\left( {{a^3} - {b^3}} \right)} \over {a\left( {a + b} \right) + {b^2}}}\,\,\,\,\,{\rm{for}}\,\,\,\,\left( {a,b} \right) = \left( {9,8} \right)\left. \matrix{ 2\left( {{a^3} - {b^3}} \right) = 2\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\,\,\, \hfill \cr ...” March 3, 2019 fskilnik@GMATH posted a reply to When defined, the expression (x^2-y^2)/(xy)-(xy-y^2)/(xy-x^2 in the Problem Solving forum “$$? = \frac{{{x^2} - {y^2}}}{{xy}} - \frac{{xy - {y^2}}}{{xy - {x^2}}}\,\,\,$$ $$\frac{{xy - {y^2}}}{{xy - {x^2}}} = \frac{{y\left( {x - y} \right)}}{{x\left( {y - x} \right)}} = \underleftrightarrow {\frac{{ - y\left( {y - x} \right)}}{{x\left( {y - x} \right)}}} = \frac{{ - y}}{x}$$ $$? = ...” March 3, 2019 fskilnik@GMATH posted a new topic called If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is: in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/9QDKH2xG/03-Mar19-12s.gif Answer: _____(C)__” March 3, 2019 fskilnik@GMATH posted a reply to If line AC bisects angle BCD, what is the measure of angle A in the Problem Solving forum “https://i.postimg.cc/L6zxMXRK/03-Mar19-9h.gif$$? = x\Delta BCE\,\,:\,\,\,20 + x = 180 - \left( {110 + 20} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 30$$The correct answer is (B). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” March 3, 2019 fskilnik@GMATH posted a new topic called If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/cJWTHNxg/03-Mar19-11p.gif Answer: ______(A)__” March 3, 2019 fskilnik@GMATH posted a new topic called When defined, the expression (x^2-y^2)/(xy)-(xy-y^2)/(xy-x^2 in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/sgHDf39K/03-Mar19-8f.gif Answer: _____(A)__” March 3, 2019 fskilnik@GMATH posted a new topic called If line AC bisects angle BCD, what is the measure of angle A in the Problem Solving forum “GMATH practice exercise (Quant Class 1) If line AC bisects angle BCD, what is the measure of angle ADC? https://i.postimg.cc/m2qQcWwZ/03-Mar19-6y.gif (A) 20 degrees (B) 30 degrees (C) 40 degrees (D) 45 degrees (E) 50 degrees Answer: ____(B)__” March 3, 2019 fskilnik@GMATH posted a new topic called What is the value of (2-1/3)(1+1/4)^(-1)(1+2/5)? in the Problem Solving forum “GMATH practice exercise (Quant Class 1) https://i.postimg.cc/br4jnvr9/03-Mar19-3q.gif Answer: _____(D)__” March 3, 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 Ian Stewart posted a reply to Is the standard deviation of Set A greater than or equal to in the Data Sufficiency forum “If you multiply all of the values in a set by some constant k, you will multiply the mean, median, range and standard deviation of that set by k. So here, if we multiply everything in set A by 1/4, we will make the standard deviation 1/4 of its previous value. Since standard deviation is always zero ...” March 2, 2019 GMATGuruNY posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum “$$(2^{(1-x)})^2$$ = $$2^{2-2x}$$ = $$2^2/2^{2x}$$ = $$4/2^{2x}$$ We need to know the value of $$2^{2x}$$: $$2^{4x}=3,600$$ $$(2^{2x})^2=3,600$$ $$2^{2x}= 60$$ Substituting $$2^{2x}= 60$$ into $$4/2^{2x}$$, we get: 4/60 = 1/15 The correct answer is B.” March 2, 2019 Ian Stewart posted a reply to Is the area of Circle A greater than the area of Circle B? in the Data Sufficiency forum “Strange question. The ratio of circumference to diameter for every circle in the universe is π, so Statement 1 tells you nothing. Circle A''s radius is half its own diameter, so if it is also half of B''s diameter, they have the same radius, and thus the same area, so Statement 2 is sufficient ...” March 2, 2019 Ian Stewart posted a reply to In a certain school, there are 160 boys and 240 girls. If 15 in the Problem Solving forum “This is a weighted average problem, where 15% and 25% are the averages of each group. We can draw a number line with the three averages: ---15------------A------25--- Since the ratio of boys to girls is 2 to 3, the overall average A will divide the total distance above in a 3 to 2 ratio, so ...” March 2, 2019 Ian Stewart posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum “Alternatively: 2^(4x) = 3600 2^(2x) = 60 2^x = √60 So (2^(1-x))^2 = (2 / 2^x)^2 = (2/√60)^2 = 4/60 = 1/15” March 2, 2019 Ian Stewart posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum “2^(4x) = 3600, so (2^2)^2x = 3600, and 4^(2x) = 3600. Taking square roots, 4^x = 60. We want to find the value of (2^(1-x))^2 = (2^2)^(1-x) = 4^(1-x) = 4^1 * 4^(-x) Since 4^x = 60, 4^(-x) is equal to 1/60, so 4^1 * 4^(-x) = 4 * (1/60) = 4/60 = 1/15” March 2, 2019 GMATGuruNY posted a reply to Car B starts at point X and moves clockwise around a circula in the Problem Solving forum “π ≈ 3. Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C. Circumference of track = 20π ≈ 60 miles. In 10 hours, distance for B = 2*10 = 20 miles. 60-20 = 40 miles between A and B. A and B now ...” March 2, 2019 fskilnik@GMATH posted a reply to From the figure shown, each of N people was asked to take 7 in the Problem Solving forum “https://i.postimg.cc/1XW4BFjw/01-Mar19-9b.gif$$?\,\, = \,\,\left( {\# \,\,{\rm{possible}}\,\,\Delta \,\,{\rm{equilateral}}\,\,{\rm{configurations}}} \right)\,\,{\rm{ + }}\,\,{\rm{1}}? = 15 + 1 = 16$$The correct answer is (D). We follow the notations and rationale taught in the ...” March 1, 2019 fskilnik@GMATH posted a reply to Oneyde and Jorge must make two reservations for a trip, in w in the Problem Solving forum “$$?\,\,\,\,:\,\,\,\# \,\,\,O,J\,\,{\rm{positions}}\,\,{\rm{with}}\,\,{\rm{restrictions}}{\rm{4 - seats}}\,\,{\rm{group}}\,\,{\rm{(left)}}\,\,{\rm{:}}\,\,{\rm{6}}\,\,{\rm{possibilities}}\,\,\,\left\{ \matrix{ \,\left( {O,J,e,e} \right)\,\,{\rm{or}}\,\,\left( {J,O,e,e} \right) \hfill \cr ...” March 1, 2019 fskilnik@GMATH posted a new topic called Oneyde and Jorge must make two reservations for a trip, in w in the Problem Solving forum “GMATH practice exercise (Quant Class 18) https://i.postimg.cc/W31dkS9T/01-Mar19-12a.gif Oneyde and Jorge must make two reservations for a trip, in which only 9 seats are still available, all of them in row F (see figure). If they want to sit next to each other, without being separated by ...” March 1, 2019 fskilnik@GMATH posted a new topic called From the figure shown, each of N people was asked to take 7 in the Problem Solving forum “GMATH practice exercise (Quant Class 18) https://i.postimg.cc/prJBksfr/01-Mar194z.gif From the figure shown, each of N people will be asked to take 7 points out, so that the 3 points left form vertices of an equilateral triangle. If all of them proceed correctly, what is the minimum value of ...” March 1, 2019 fskilnik@GMATH posted a reply to What is the value of k? in the Data Sufficiency forum “https://i.postimg.cc/JhzCQJM1/01-Mar19-4q.gif $$? = k\,\,\,\leftGMATH method. Regards, Fabio.” March 1, 2019 GMATGuruNY posted a reply to Which of following satisfies the inequality (2x-49)(x^2+6x+1 in the Problem Solving forum “The two factors must have DIFFERENT SIGNS. Each of the answer choices will yield a positive value for x² + 6x + 10. Thus, the correct answer must yield a negative value for 2x-49. Only A is viable: (2*24) - 49 = -1. The correct answer is A.” March 1, 2019 GMATGuruNY posted a reply to Andrew bought pizzas for his swim team. Pepperoni pizzas in the Problem Solving forum “Posted and answered about a week ago: https://www.beatthegmat.com/andrew-bought-pizzas-for-his-swim-team-pepperoni-pizzas-cos-t306615.html#827261” March 1, 2019 GMATGuruNY posted a reply to The three squares above share vertex A with AF = FE and AE = in the Problem Solving forum “Let AF=FE=1, with the result that AE=ED=2: https://i.postimg.cc/2qmj2KbL/probability-and-three-squares.png As the figure illustrates: shaded region = 1+1+1 = 3 ABCD = 4*4 = 16 shaded/ABCD = 3/16 The correct answer is D.” March 1, 2019 GMATGuruNY posted a reply to In a certain clothing store, the most expensive pair of in the Problem Solving forum “Option D indicates that 12 pairs of cheap socks can be bought, not 9. Unfortunately, 9 is not among the answer choices. The OA implies that each pair of cheap socks costs not 2 but 1.50. Because 1.50 is not an integer value, the brute-force approach is a bit tricky here.” March 1, 2019 GMATGuruNY posted a reply to In a certain clothing store, the most expensive pair of in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the number of cheap pairs that can be purchased for 18. When the correct answer is plugged in, the number of expensive pairs that can be purchased will be 3 less than the number of cheap pairs that can be purchased. B will yield an ugly price for each ...” February 28, 2019 Brent@GMATPrepNow posted a reply to In a certain clothing store, the most expensive pair of in the Problem Solving forum “Let C = price of one pair of the CHEAPEST socks So, 2C - 1 = price of one pair of the MOST EXPENSIVE socks A customer notices that for exactly 18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. As a word equation, we can write: (# of pairs of EXPENSIVE ...” February 28, 2019 fskilnik@GMATH posted a reply to If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab? in the Problem Solving forum “$$? = \,\,ab{2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,{2^{a + 1}} \cdot {3^{b - 1}}\, = {\left( {2 \cdot {3^2}} \right)^b} = {2^b} \cdot {3^{2b}}{2^{a + 1 - b}} = {3^{2b - \left( {b - 1} \right)}}\,\,\,\,\,\mathop ...” February 28, 2019 fskilnik@GMATH posted a reply to Planifying the lateral surface area of a cone, we get the ci in the Problem Solving forum “https://i.postimg.cc/0Qyn3DSH/28-Feb19-4y.gif $$?\,\, \cong \,\,h$$ $${\text{circular}}\,\,{\text{base}}\,{\text{of}}\,\,{\text{cone}}\,\,:\,\,\,\,2\pi r\,\, = \,\,\frac{{{{160}^ \circ }}}{{{{360}^ \circ }}}\left( {2\pi \cdot 18} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,r = \frac{{16 \cdot ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Two positive numbers differ by 12 and their reciprocals in the Problem Solving forum “Two positive numbers differ by 12 Let x = the smaller number So x + 12 = the larger number NOTE: our goal is to find the value of x(x + 12) Their reciprocals differ by 4/5 We get: 1/x - 1/(x+12) = 4/5 Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5 Multiply both sides by 5 to get: 5 ...” February 28, 2019 Brent@GMATPrepNow posted a reply to In a town of 8,000 residents, 65 percent of all residents in the Problem Solving forum “Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of residents, and the two characteristics are: ...” February 28, 2019 fskilnik@GMATH posted a new topic called What is the value of k? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.postimg.cc/QNk4tN8b/28-Feb19-9j.gif What is the value of k? (1) x = 2 (2) y^2 = 3 Answer: ____(C)___” February 28, 2019 fskilnik@GMATH posted a new topic called If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab? in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/SsG5YcFy/28-Feb19-6t.gif Answer: ____(E)__” February 28, 2019 fskilnik@GMATH posted a new topic called Planifying the lateral surface area of a cone, we get the ci in the Problem Solving forum “GMATH practice exercise (Quant Class 11) https://i.postimg.cc/zBvv4GGk/28-Feb19-3w.gif Planifying the lateral surface area of a cone, we get the circular sector with center O and radius 18 shown in the figure. Which of the following is closest to the length of the height of this cone? (A) ...” February 28, 2019 fskilnik@GMATH posted a reply to If the line segment AB is one of the sides of a regular poly in the Data Sufficiency forum “https://i.postimg.cc/zvXz514z/27-Feb19-9k.gif$${\rm{regular}}\,\,N{\rm{ - polygon}}\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} } \right)? = N\left( 1 \right)\,\,\alpha = {30^ \circ }\,\,\,\, \Rightarrow \,\,\,\angle AOB = {60^ \circ }\,\,\,\left( {{\rm{central}}\,\,{\rm{angle}}} ...” February 28, 2019 fskilnik@GMATH posted a reply to What is the value of DE/FG ? in the Data Sufficiency forum “$$\Delta ADE\,\,\, \cong \,\,\,\Delta AFG\,\,\, \cong \,\,\,\Delta ABC$$ $$? = \frac{{DE}}{{FG}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,?\,\, = \,\,\,\Delta ADE:\Delta AFG\,\,\,{\text{ratio}}\,\,{\text{of}}\,\,{\text{similarity}}\,\,{\text{ = }}\,\,\,\frac{{AD}}{{AF}}\,\,\left( { = ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum “Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...” February 28, 2019 Brent@GMATPrepNow posted a reply to A certain club has 20 members. What is the ratio of the in the Problem Solving forum “5-member committees Since the order in which we select the committee members does not matter, we can use COMBINATIONS We can select 5 people from 20 people in 20C5 ways 20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) 4-member committees Since the order in which we select the committee members ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Train A and Train B began traveling towards each other from in the Problem Solving forum “This is a SHRINKING GAP question. Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, 35 mph + 25 mph = 60 mph So, the gap CLOSES at a rate of 60 mph Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM ...” February 28, 2019 fskilnik@GMATH posted a reply to A large rectangular decorative panel of 45 meters (horizonta in the Problem Solving forum “$${\rm{panel}}\,\,:\,\,\,4500\,{\rm{cm}}\,\, \times \,\,\,600\,{\rm{cm}}M\,\,{\rm{squares}}\,\,{\rm{:}}\,\,\,k\,{\rm{cm}}\,\, \times \,\,\,k\,{\rm{cm}}\,\,\,{\rm{each}}\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right){\rm{?}}\,\, = \,\,\,\min \left( M \right)\left. ...” February 28, 2019 GMATGuruNY posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum “Use the following equation: (machines)(time) / output = (machines)(time) / output In the equation above: Machines and time are INVERSELY PROPORTIONAL. As the number of machines increases, the amount of time required to produce the same output decreases. Machines and output are DIRECTLY ...” February 28, 2019 GMATGuruNY posted a reply to The restorative power of sleep is graphically approximated b in the Problem Solving forum “Multiplying the equation by -1, we get: y = x² - 16x - 36 y = (x-18)(x+2) The restorative power -- the value of y -- is equal to 0 when x=18 or x=-2. Since the time cannot be a negative value, only x = 18 hours is viable. The correct answer is E.” February 28, 2019 GMATGuruNY posted a reply to In June 1989, what was the ratio of the number of sales tran in the Data Sufficiency forum “What is (June X)/(June Y)? Statement 1: In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (June X)/(May Y) = 150/100 = 3/2. INSUFFICIENT. Statement 2: In June 1989, Salesperson Y made 25 percent more sales transactions than in May ...” February 28, 2019 fskilnik@GMATH posted a new topic called If the line segment AB is one of the sides of a regular poly in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.postimg.cc/13f7VYDv/27-Feb19-4q.gif Answer: ____(A)__” February 28, 2019 Brent@GMATPrepNow posted a reply to In 1990 the budgets for projects Q and V were660,000 and in the Problem Solving forum
“One approach is to treat this is a rate question. In 1990 the GAP BETWEEN V''s budget and Q''s budget was $120,000 ($780,000 - $660,000 =$120,000) Each year, the budget for Q increased by $30,000 and the budget for V decreased by$10,000. In other words, the GAP BETWEEN the budgets ...”
February 28, 2019
fskilnik@GMATH posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum
“Hi! I have made Ian know about your interest in his materials a minute ago. I believe he will be here soon to contact you. Regards and have great studies with his (I am certain) outstanding collection, Fabio.”
February 27, 2019
fskilnik@GMATH posted a new topic called What is the value of DE/FG ? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 17) https://i.ibb.co/tDdzQZJ/27-Feb19-3j.gif What is the value of DE/FG ? (1) AB/AD = 5 (2) AD = FB Answer: ____(C)__”
February 27, 2019
fskilnik@GMATH posted a new topic called A large rectangular decorative panel of 45 meters (horizonta in the Problem Solving forum
“GMATH practice exercise (Quant Class 16) A large rectangular decorative panel of 45 meters (horizontal dimension) by 6 meters (vertical dimension) is to be completely divided into M identical squares, all of them with horizontal and vertical edges. If the smallest measure of length considered for ...”
February 27, 2019
fskilnik@GMATH posted a reply to During a 3h-experiment, the number of bacteria increased fro in the Problem Solving forum
“$$f\left( t \right) = a \cdot {b^t}\,\,\,{\rm{bacteria}}\,\,\,\,\,\left( {{\rm{at}}\,\,t \ge 0\,\,{\rm{hours}}} \right)$$ $$? = f\left( {{1 \over 2}} \right) = a \cdot \sqrt b$$ $$\left( {0\,;\,{{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,{10^4} = a \cdot ...” February 27, 2019 fskilnik@GMATH posted a reply to In the rectangular coordinate system, what is the area of th in the Problem Solving forum “https://i.ibb.co/drKdnk4/26-Feb19-5z.gif$$? = {S_{{\rm{shaded}}}}\,\,\,:\,\,\,\,\left\{ \matrix{ \,xy > 0\, \hfill \cr \,0 < y < 2\,\,\,\, \hfill \cr \,x < y + 1 \hfill \cr} \right.\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\,\,\left\{ \matrix{ \,x > 0\, \hfill \cr \,0 ...”
February 27, 2019
fskilnik@GMATH posted a reply to In the rectangular coordinate system, what is the area of th in the Problem Solving forum
“The "image of the system" is part of the solution! As you will see below, it is almost the whole solution itself! Regards, Fabio.”
February 27, 2019
fskilnik@GMATH posted a reply to If x, y, and z are integers such that 67500 is divisible by in the Problem Solving forum
“$$? = \max \left( {3x + 2y + z} \right)\,\,\,\left( * \right)$$ $$x,y,z\,\,\mathop \ge \limits^{\left( * \right)} \,\,0\,\,\,{\rm{ints}}\,\,\,\left( {**} \right)$$ $$67500 = \underleftrightarrow {675 \cdot 100} = 25 \cdot 27 \cdot 4 \cdot 25 = {2^2} \cdot {3^3} \cdot {5^4}$$ $$54 = 2 \cdot 27 ...” February 27, 2019 fskilnik@GMATH posted a reply to In the equality above, A,B,C are positive integers. What is in the Problem Solving forum “$$A,B,C\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right){{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}? = 2A + 3B - 4C\left. \matrix{ B + {1 \over {C + 1}}\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,0 < \,{1 ...”
February 27, 2019
fskilnik@GMATH posted a reply to What is the value of a+b? in the Data Sufficiency forum
“$$? = a + b$$ $$\left( 1 \right)\,\,a\left( {a + b - 2} \right) = 91\,\,\,\,:\,:\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {91,\, - 88} \right)\,\,\,\, \Rightarrow \,\,\,? = 3\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,92} \right)\,\,\,\, ...” February 27, 2019 GMATGuruNY posted a reply to How many whole numbers between 100 and 400, inclusive, conta in the Problem Solving forum “(integers with the digit 2) = (all integers between 100 and 399, inclusive) - (integers without the digit 2) All integers between 100 and 399, inclusive: For any set of consecutive integers, count = biggest - smallest + 1. In this case: count = 399-100+1 = 300 Integers without the digit 2: ...” February 27, 2019 GMATGuruNY posted a reply to A square playground has the same area as a rectangular in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent a side of the square. Since the dimension of the rectangular playground are INTEGER values, the correct answer is probably also an integer. When the correct answer is plugged in, the square and the rectangle will have the same area. D: 50, implying ...” February 27, 2019 GMATGuruNY posted a reply to Two hoses are pouring water into an empty pool. Hose 1 alone in the Problem Solving forum “Let the pool = 12 gallons. Since Hose 1 takes 6 hours to fill the 12-gallon pool, the rate for Hose 1 = w/t = 12/6 = 2 gallons per hour. Since Hose 2 takes 4 hours to fill the 12-gallon pool, the rate for Hose 2 = w/t = 12/4 = 3 gallons per hour. Since the combined rate for the two hoses = 2+3 = ...” February 27, 2019 fskilnik@GMATH posted a new topic called In the rectangular coordinate system, what is the area of th in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.ibb.co/NLBX1Wj/26-Feb19-7d.gif Answer: ____(C)__” February 26, 2019 fskilnik@GMATH posted a new topic called During a 3h-experiment, the number of bacteria increased fro in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.ibb.co/QDJ1ShL/26-Feb19-4q.gif During a 3h-experiment, the number of bacteria increased from 10^4 (at the start) to 8 times this value (at the end), according to a biological law associated with an exponential function (as shown), where a and ...” February 26, 2019 fskilnik@GMATH posted a new topic called If x, y, and z are integers such that 67500 is divisible by in the Problem Solving forum “GMATH practice exercise (Quant Class 16) If x, y, and z are integers such that 67500 is divisible by (2^x)(3^y)(5^z) and (2^x)(3^y)(5^z) is NOT a multiple of 54, what is the maximum possible value of 3x+2y+z? (A) 15 (B) 14 (C) 13 (D) 12 (E) less than 12 Answer: _____(B)__” February 26, 2019 GMATGuruNY posted a reply to What is the value of a+b? in the Data Sufficiency forum “Statements combined: Adding the two equations, we get: a² + b²+ 2ab - 2a - 2b = 63 (a+b)² - 2(a+b) = 63 (a+b)(a+b-2) = 63 Let x = a+b. Substituting x=a+b into (a+b)(a+b-2) = 63, we get: (x)(x-2) = 63 x² - 2x - 63 = 0 (x-9)(x+7) = 0 x=9 or x=-7 Since x=a+b, it is possible that ...” February 26, 2019 GMATGuruNY posted a reply to On a Saturday night, each of the rooms at a certain motel in the Problem Solving forum “If 10 rooms are rented for 40 instead of 60 -- a decrease of 20 per room -- the total decrease = 10*20 = 200. Since the value in blue constitutes a 25% reduction in the total rent, it must be equal to 1/4 of the total rent: 200 = (1/4)R 800 = R. The correct answer is B.” February 26, 2019 fskilnik@GMATH posted a new topic called In the equality above, A,B,C are positive integers. What is in the Problem Solving forum “GMATH practice exercise (Quant Class 1) https://i.ibb.co/C7pD425/26-Feb19-3w.gif Answer: ____(C)__” February 26, 2019 fskilnik@GMATH posted a new topic called What is the value of a+b? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) What is the value of a+b ? (1) a^2+ab−2a=91 (2) b^2+ab−2b=−28 Answer: ____(E)__” February 26, 2019 GMATGuruNY posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum “How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit? If c=1 and r=2 -- implying that the cost per umbrella = 1 and that the retail price per umbrella = 2 -- then 100% profit will be yielded only if ALL of the umbrellas are sold at ...” February 26, 2019 Brent@GMATPrepNow posted a reply to Is xy+zt+yz+tx positive? in the Data Sufficiency forum “Target question: Is xy + zt + yz + tx positive? Statement 1: |x| = |y| = |z| = t Let''s TEST some values. There are several values of x, y, z and t that satisfy statement 1. Here are two: Case a: x = y = z = t = 1. In this case, xy + zt + yz + tx = (1)(1) + (1)(1) + (1)(1) + (1)(1) = 4. ...” February 26, 2019 Brent@GMATPrepNow posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum “This is a tough one to use the INPUT-OUTPUT approach, but here is goes: Let c = 2 (it cost 2 to make each umbrella) Let x = 10 (we make 10 umbrellas) Let r = 5 (the retail price is 5 per umbrella) Let b = 0 (the below-cost sale price is 0 per umbrella) So, the manufacturer made 10 ...” February 26, 2019 GMATGuruNY posted a reply to On rainy mornings, mo drinks exactly N cups of hot chocolate in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the number of rainy days. When the correct answer is plugged in, the total number of cups = 26. B: 3 rainy days, implying 4 non-rainy days Since 5 cups of tea are consumed are on each of the 4 non-rainy days, the total number of tea cups = 5*4 = 20. ...” February 26, 2019 GMATGuruNY posted a reply to It takes Carlos 9 minutes to drive from home to work at an in the Problem Solving forum “(new rate)/(old rate) = (6 miles per hour)/(22 miles per hour) = 6/22 = 3/11. Rate and time have a RECIPROCAL relationship. Since the new rate is 3/11 of the old rate, the new time must be 11/3 of the old time: (11/3)(9 minutes) = 33 minutes. The correct answer is B.” February 26, 2019 GMATGuruNY posted a reply to A is the set of 6-digit positive integers whose first three in the Problem Solving forum “The GMAT is unlikely to test divisibility by 7. An integer of the form XYZXYZ must be divisible by 7, but this issue seems irrelevant to the GMAT. For this reason, I''ve replaced answer choice A with the value in red: To determine whether an integer is divisible by 11: 1. From the left to ...” February 26, 2019 fskilnik@GMATH posted a reply to What is the difference between the areas of the squares ABCD in the Data Sufficiency forum “$$?\,\, = \,\,{S_{{\rm{ABCD}}}} - {S_{{\rm{EFGC}}}}$$(Click on the image to have it "zoomed"!) https://i.ibb.co/KhpKxCh/25-Feb19-6r.gif$$\left. \matrix{ \left( {1 + 2} \right)\,\,\,\,? = \,{\left( {5k} \right)^2} - {\left( {3k} \right)^2} = 16{k^2} \hfill \cr 30 = ...”
February 26, 2019
fskilnik@GMATH posted a reply to Is xy+zt+yz+tx positive? in the Data Sufficiency forum
“$$\underline {xy} + \underline{\underline {zt}} + \underline {yz} + \underline{\underline {tx}} \,\,\mathop > \limits^? \,\,0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,y\left( {x + z} \right) + t\left( {z + x} \right) = \left( {x + z} \right)\left( {y + t} \right)\,\,\,\mathop > \limits^? ...” February 26, 2019 fskilnik@GMATH posted a reply to If x^3 (x^2+y^2) = z^2 , is xyz = 0 ? in the Data Sufficiency forum “$${x^3}\left( {{x^2} + {y^2}} \right) = {z^2}\,\,\,\,\,\left( * \right)xyz \,\, \mathop = \limits^? \,\,0\left( {1 + 2} \right)\,\,\left\{ \matrix{ \,{y^3}\left( {{y^2} + {z^2}} \right) = {x^2}\,\,\left( * \right) \hfill \cr \,{z^3}\left( {{z^2} + {x^2}} \right) = ...”
February 26, 2019
fskilnik@GMATH posted a new topic called If x^3(x^2+y^2) = z^2 , is xyz = 0 ? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) If x^3 (x^2+y^2) = z^2 , is xyz = 0 ? (1) y^3 (y^2+z^2) = x^2 (2) z^3 (z^2+x^2) = y^2 Answer: ____(E)__”
February 25, 2019
fskilnik@GMATH posted a new topic called Is xy+zt+yz+tx positive? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) Is xy+zt+yz+tx positive? (1) |x| = |y| = |z| = t (2) x+y+z+t = 0 Answer: ____(B)__”
February 25, 2019
GMATGuruNY posted a reply to What is the difference between the areas of the squares ABCD in the Data Sufficiency forum
“Statement 1: Case 1: DC=10 and EC=6, with the result that CDE = (1/2)(10)(6) = 30 In this case, ABCD-EFGC = 10² - 6² = 100 - 36 = 64. Case 2: DE=20 and EC=3, with the result that CDE = (1/2)(20)(3) = 30 In this case, ABCD-EFGC = 20² - 3² = 400 - 9 = 391. Since ABCD-EFGC can be different ...”
February 25, 2019
fskilnik@GMATH posted a new topic called What is the difference between the areas of the squares ABCD in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 15) https://i.ibb.co/9mxGjhk/25-Feb19-4q.gif What is the difference between the areas of the squares ABCD and EFGC, in that order? (1) The area of the shaded triangle CDE is 30. (2) The ratio of the areas of the squares ABCD and EFGC, in that order, ...”
February 25, 2019
fskilnik@GMATH posted a reply to Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum
“ $$?\,\,\mathop = \limits^{\left( * \right)} \,\,\,\# \,\,\left( {{\text{odd,even,odd,even,odd,even,odd,even,odd}}} \right)\,\,{\text{tuples}}$$ $$\left( * \right)\,\,{\text{must}}\,\,{\text{start}}\,\,{\text{and}}\,\,{\text{finish}}\,\,{\text{with}}\,\,{\text{odd numbers}}\,\,\,\left( ...” February 25, 2019 fskilnik@GMATH posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “$$?\,\,\,\,:\,\,\,\# N\,,\,\,N \in \leftGMATH method. Regards, Fabio.”
February 25, 2019
“$$?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)$$ $${\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow ...” February 25, 2019 fskilnik@GMATH posted a reply to If G is a function defined in the positive integers, such th in the Data Sufficiency forum “$$? = G\left( {G\left( {2019} \right)} \right)\left( 1 \right)\,\,\,\left\{ \matrix{ \,G\left( {G\left( {m + n} \right)} \right) = m + n\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right) \hfill \cr \,\,\,\,\,\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2018,1} \right) \hfill \cr} ...”
February 25, 2019
fskilnik@GMATH posted a reply to For each positive integer n, the nth positive triangular num in the Problem Solving forum
“$${T_n} = 1 + 2 + \ldots + n\,\,\mathop = \limits^{\left( * \right)} \,\,{{n \cdot \left( {n + 1} \right)} \over 2}\,\,\,\,\,\,\,\left( {n \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\,\,\,\,\,\,\leftGMATH method. Regards, Fabio.” February 25, 2019 GMATGuruNY posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “For any set of consecutive integers: count = biggest - smallest + 1 Thus: Number of two-digit integers between 10 and 99, inclusive = 99-10+1 = 90. Of these 90 consecutive integers, 1 of every 3 will be a multiple of 3, implying that 2/3 will NOT be divisible by 3: (2/3)(90) = 60. Of these ...” February 25, 2019 Brent@GMATPrepNow posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “After about 30 seconds, I recognized that I couldn''t see a nice straightforward solution (one that doesn''t involve considering multiple cases), so I had 3 options: 1) Keep searching for a nice straightforward solution 2) Guess and move on 3) List the possible outcomes Since the answer ...” February 25, 2019 Brent@GMATPrepNow posted a reply to Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum “ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8 Take the task of removing the 9 chips and break it into stages. Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways Stage 2: Select an EVEN number to be the 2nd selection ...” February 25, 2019 fskilnik@GMATH posted a new topic called Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum “GMATH practice exercise (Quant Class 18) Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. ...” February 25, 2019 fskilnik@GMATH posted a new topic called How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 Answer: ____(B)__” February 25, 2019 Brent@GMATPrepNow posted a reply to All assets in Karina's investment portfolio are divided betw in the Problem Solving forum “Let''s say Karina''s entire portfolio is worth 100 altogether. So, we want to divide this 100 into four integer amounts: w, x, y, z, where w < x < y < z, and we want to minimize the value of z In order to MINIMIZE the value of the z, we must MAXIMIZE the values of w, x, and y. Now ...” February 25, 2019 Brent@GMATPrepNow posted a reply to Vivian drives to her sister’s house and back. She takes th in the Problem Solving forum “One approach is to assign a "nice" value (one that works well with 50 mph and 70 mph) to the distance her sister''s house. So, let''s say the distance is 350 miles Average speed = (total distance traveled)/(total travel time) TOTAL distance = 350 miles + 350 miles = 700 miles ...” February 25, 2019 GMATGuruNY posted a reply to 2016 OG CR 30 in the Critical Reasoning forum “Why do people who do regular volunteer work live longer? The argument concludes that ENDORPHINS are the cause. One way to weaken this conclusion is to suggest an ALTERNATE CAUSE. D: People tend not to become involved in regular volunteer work unless they are healthy and energetic to begin with. ...” February 25, 2019 GMATGuruNY posted a reply to Vivian drives to her sister’s house and back. She takes th in the Problem Solving forum “When the SAME DISTANCE is traveled at two different speed, the average speed for the entire trip will be just a little less than the average of the two speeds. The reason: The trip at the lower speed takes longer than the trip at the higher speed. Since more time is spent at the lower speed, the ...” February 25, 2019 GMATGuruNY posted a reply to Before January, the price of a dress was D and the price of in the Problem Solving forum “Let H=100 and D=500. D increased by 40% = 500 + (40/100)(500) = 500+200 = 700. H increased by 50% = 100 + (50/100)(100) = 100+50 = 150. New sum = 700+150 = 850. Amount paid = new sum discounted by 30% = 850 - (30/100)(850) = 850-255 = 595. The question stem asks for the amount paid. The ...” February 25, 2019 GMATGuruNY posted a reply to All assets in Karina's investment portfolio are divided betw in the Problem Solving forum “To MINIMIZE the percent for the largest balance, MAXIMIZE the percents for the 3 smallest balances. We can PLUG IN THE ANSWERS, which represent the percent in the largest balance. When the correct answer is plugged in, the 4 percents will sum to 100%. Since the question stem asks for the smallest ...” February 25, 2019 fskilnik@GMATH posted a new topic called You have access to an unlimited number of each of the follow in the Problem Solving forum “GMATH practice exercise (Quant Class 3) You have access to an unlimited number of each of the following coins: pennies, nickels, dimes and quarters. Which of the following amounts CAN be made using exactly 6 of these coins? I. 76 cents II. 81 cents III. 29 cents IV. 101 cents (A) None of ...” February 24, 2019 fskilnik@GMATH posted a new topic called If G is a function defined in the positive integers, such th in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) If G is a function defined in the positive integers, such that G(k) is a positive integer for each positive integer k, what is the value of G(G(2019)) ? (1) G(G(m+n))=m+n , for every positive integers m,n. (2) G(n)=m implies G(m)=n, for every positive ...” February 24, 2019 fskilnik@GMATH posted a new topic called For each positive integer n, the nth positive triangular num in the Problem Solving forum “GMATH practice exercise (Quant Class 17) https://i.ibb.co/qjVrNkW/24-Feb19-4z.gif For each positive integer n, the nth positive triangular number is equal to the number of dots in the triangular arrangement with n dots on a side. The first positive triangular numbers are 1, 3, 6, 10, 15, and ...” February 24, 2019 GMATGuruNY posted a reply to In a certain class, the ratio of girls to boys is 5:4. How m in the Data Sufficiency forum “g:b = 5:4 = 10:8 = 15:12 = 20:16 = 25:20... Statement 1: In other words, 4 boys are equal to 20% of the current number of boys, implying the blue ratio above, since 20% of 20 boys = 4 boys. In the blue ratio above, the number of girls = 25. SUFFICIENT. Statement 2: Test the smaller red ...” February 24, 2019 Brent@GMATPrepNow posted a reply to In a certain class, the ratio of girls to boys is 5:4. How m in the Data Sufficiency forum “ Given: In a certain class, the ratio of girls to boys is 5:4. Let G = number of girls in the class Let B = number of boys in the class We can write: G/B = 5/4 Cross multiply to get: 4G = 5B Rearrange to get: 4G - 5B = 0 Target question: What is the value of G Statement 1: If four ...” February 24, 2019 Brent@GMATPrepNow posted a reply to Kim has 40 percent more money than Sal and Sal has 20 in the Problem Solving forum “Let x = Phil''s money Sal has 20 percent LESS money than Phil So, Sal''s money = (Phil''s money) - (20% Phil''s money) = x - (20% of x) = x - 0.2x = 0.8x Kim has 40 percent more money than Sal So, Kim''s money = (Sal''s money) + (40% Sal''s money) = (0.8x) + (40% of 0.8x) = ...” February 24, 2019 Brent@GMATPrepNow posted a reply to A straight line in the xy-plane has a slope of 2 and a in the Problem Solving forum “The question conveniently gives us the information to write the equation of the line in slope y-intercept form, y = mx + b, where m = slope and b = the y-intercept. Line in the xy-plane has a slope of 2 and a y-intercept of 2 So, the equation of the line is: y = 2x + 2 On this line, what is ...” February 24, 2019 Brent@GMATPrepNow posted a reply to If y >= 0, What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Given: y ≥ 0 Statement 1: |x - 3| ≥ y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 10 and y = 2. We get |10 - 3| ≥ 2, which evaluates to be 7 ≥ 2, which satisfies ...” February 23, 2019 Brent@GMATPrepNow posted a reply to The total of company C's assets in 1994 was 300% greater in the Problem Solving forum “The total of company C''s assets in 1992 was N dollars Company C''s assets in 1993 was 400% greater than the total in 1992 So, 1993 assets = (1992 assets) + (400% of 1992 assets) = (N) + (400% of N) = (N) + (400/100 x N) = N + 4N = 5N Company C''s assets in 1994 was 300% greater than the ...” February 23, 2019 GMATGuruNY posted a reply to The total of company C's assets in 1994 was 300% greater in the Problem Solving forum “Let N dollars in 1992 = 1. Since the assets in 1993 are 300% greater than the N dollars in 1992, the assets in 1993 = 1 + (300% of 1) = 1+3 = 4. Since the assets in 1994 are 400% greater than the assets in 1993, the assets in 1994 = 4 + (400% of 4) = 4 + 16 = 20. The question stem asks for ...” February 23, 2019 Brent@GMATPrepNow posted a reply to At a bakery, the price of a bagel ranges between 0.65 and  in the Problem Solving forum “The least expensive price for a bagel is 0.65 If a customer purchases 12 bagels (at 0.65 each), then he/she receives 13 bagels. So, the minimum amount that a customer could pay to receive 13 bagels = 12 x 0.65 = 7.80 Answer: B Cheers, Brent” February 23, 2019 GMATGuruNY posted a reply to Andrew bought pizzas for his swim team. Pepperoni pizzas cos in the Problem Solving forum “13x + 17y = 184. Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104... Multiple of 17: 17, 34, 51, 68, 85, 102, 119.... The values in blue sum to 184. Since 65/13 = 5 and 119/17 = 7, the number of pizzas = 5+7 = 12. The correct answer is A.” February 23, 2019 GMATGuruNY posted a reply to Nathan took out a student loan for 1200 at 10 percent in the Problem Solving forum “Since the 10% rate is compounded annually, the amount of interest increases by 10% each year: First-year interest = 10% of 1200 = 120. Second-year interest = (first-year interest) + 10% = 120 + 12 = 132. Third-year interest = (second-year interest) + 10% = 132 + 13.2 = 145.2. Total interest = ...” February 22, 2019 GMATGuruNY posted a reply to Ten theater students are to begin work on a set for a 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.” February 22, 2019 fskilnik@GMATH posted a reply to In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum “https://i.ibb.co/HHMzBxX/21-Feb19-4wq.gif$$?\,\, \cong \,\,\pi {r^2}$$Point O is equidistant from the rays AM and AN, hence AO must be contained in the angle bisector of angle MAN = angle BAC.$$\left\{ \matrix{ \,OM = r\,\,\,\left( {{{30}^ \circ }} \right) \hfill \cr \Delta ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to a, b, and c are positive integers. Is a+b+c an odd number? in the Data Sufficiency forum
“ Given: a, b, and c are positive integers. Target question: Is a + b + c an odd number? Statement 1: ab is an odd number No information about c. NOT SUFFICIENT Statement 2: c is an odd number No information about a or b. NOT SUFFICIENT Statements 1 and 2 combined If ab ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to In how many ways a cricket team consisting of 5 batsmen, 4 in the Problem Solving forum
“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”
February 22, 2019
Brent@GMATPrepNow posted a reply to If 1/x-1/y=1/z, what is the value of y, in terms of x and z? in the Problem Solving forum
“We can also solve the question algebraically. GIVEN: 1/x - 1/y = 1/z Multiply both sides by x to get: 1 - x/y = x/z Multiply both sides by y to get: y - x = xy/z Multiply both sides by z to get: yz - xz = yx Rearrange to get y terms on one side: yz - yx = xz Factor left side: y(z - x) = ...”
February 22, 2019
fskilnik@GMATH posted a reply to The graphs of the functions f and g are represented in In th in the Problem Solving forum
“https://i.ibb.co/rmtCdPt/21-Feb19-4v.gif $$? = g\left( {g\left( { - 1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)$$ $$A\,\, = \,\,g\left( { - 1} \right) = 4\,\,\,\leftGMATH method. Regards, Fabio.” February 22, 2019 fskilnik@GMATH posted a reply to Brenda will test-drive a vintage motor car on a circular tra in the Problem Solving forum “$$?\,\,\,:\,\,\,{\rm{approx}}.\,\,{\rm{degrees - rotation}}\,\,\,{\rm{in}}\,\,\,{\rm{1}}\,\,{\rm{min}}360\,\,{\rm{degrees - rotation}}\,\,\,\, \leftrightarrow \,\,\,\,2 \cdot \pi \cdot 300\,\,{\rm{meters}}\,\,\,\,\,\,\left( {1\,\,{\rm{lap}}} \right)10\,\,{\rm{meters}}\,\,\,\, ...”
February 22, 2019
fskilnik@GMATH posted a reply to The curve shown above is defined by the ordered-pairs (x,y) in the Problem Solving forum
“$$y = A{x^2} + 2Bx + C$$ $$A > 0\,\,:\,\,\,{\rm{parabola}}\,\,{\rm{concave}}\,\,{\rm{upward}}\,$$ $$C > 0\,\,:\,\,\,y - {\rm{intercept}}\,\,{\rm{ > }}\,\,{\rm{0}}\,\,\,\,\,\,\,\,\leftThe correct answer is (C). We follow the notations and rationale taught in the GMATH method. ...” February 22, 2019 GMATGuruNY posted a reply to In how many ways a cricket team consisting of 5 batsmen, 4 in the Problem Solving forum “From 7 batsmen, the number of ways to choose 5 = 7C5 = (7*6*5*4*3)/(5*4*3*2*1) = 21. From 6 bowlers, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15. From 3 wicketkeepers, the number of ways to choose 1 = 3. From 3 allrounders, the number of ways to choose 1 = 3. To combine these ...” February 22, 2019 GMATGuruNY posted a reply to How many different arrangements are possible to place seven in the Problem Solving forum “Let the 3 math books = A, B, C and the remaining 4 books = D, E, F, G. Since the 3 math books must be next to one another, put them together in a block: E.” February 22, 2019 GMATGuruNY posted a reply to If 1/x-1/y=1/z, what is the value of y, in terms of x and z? in the Problem Solving forum “Let x=1 and y=3/2, with the result that 1/z = 1 - 2/3 = 1/3, so z=3. Since the question stem asks for the value of y, the correct answer must yield 3/2 when x=1 and z=3. Since B and D include x-z and thus will yield a negative result, eliminate B and D. Since E includes only multiplication and ...” February 22, 2019 GMATGuruNY posted a reply to Is p^3 < p? in the Data Sufficiency forum “Statements combined: Case 1: p=0, with the result that p is an integer less than 1 In this case, p³=p, so the answer to the question stem is NO. Case 2: p=-2, with the result that p is an integer less than 1 In this case, p³ < p, so the answer to the question stem is YES. Since the answer ...” February 22, 2019 GMATGuruNY posted a reply to In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum “https://i.postimg.cc/06HLPxqC/circle-in-a-sector.png AOP passes through the center of the inscribed circle and thus must BISECT sector ACB. AB, AP and AC are all radii of sector ACB and thus are equal. The prompt indicates AB=AC=12. Thus: AP=12. As shown in the figure, AOM is a 30-60-90 ...” February 22, 2019 Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 in the Problem Solving forum “A quick solution is to assign some values to the highest paid and lowest paid workers Let 10,000 = the lowest salary LAST YEAR Let 40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = 30,000 If the annual salary of each of the 100 employees this ...” February 21, 2019 GMATGuruNY posted a reply to The sum of two integers is 27. The larger integer is 25% in the Problem Solving forum “25% greater = 1/4 greater. If the smaller integer = 4, then the larger integer = 4 + (1/4)4 = 5. The values in red imply that the two integers summing to 27 must be in a RATIO OF 4 TO 5: 4, 5 8, 10 12, 15 The case in blue sums to 27, with the result that larger-smaller = 15-12 = 3. The ...” February 21, 2019 Brent@GMATPrepNow posted a reply to The sum of two integers is 27. The larger integer is 25% in the Problem Solving forum “Let x = the smaller integer So, 1.25x = the larger integer (since the larger integer is 25% greater than the smaller integer) The sum of two integers is 27. We can write: x + 1.25x = 27 Simplify: 2.25x = 27 Solve: x = 27/2.25 IMPORTANT: What''s a nice fast way to evaluate 27/2.25? An easy ...” February 21, 2019 fskilnik@GMATH posted a new topic called Brenda will test-drive a vintage motor car on a circular tra in the Problem Solving forum “GMATH practice exercise (Quant Class 5) Brenda will test-drive a vintage motor car on a circular track with radius 300 meters, at a constant speed of 10 meters per second. If her husband Jim is at rest, at the center of this track, to film the entire test-drive, which of the following values is ...” February 21, 2019 fskilnik@GMATH posted a new topic called In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum “GMATH practice exercise (Quant Class 7) https://i.ibb.co/XyZrzVC/21-Feb19-7k.gif In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of ...” February 21, 2019 fskilnik@GMATH posted a new topic called The curve shown above is defined by the ordered-pairs (x,y) in the Problem Solving forum “GMATH practice exercise (Quant Class 13) https://i.ibb.co/yQqt4tj/21-Feb19-4p.gif The curve shown above is defined by the ordered-pairs (x,y) such that y = f(x) = Ax^2+2Bx+C, where A, B and C are given constants. If the point of tangency with the x-axis has a positive x-coordinate, which of ...” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the greatest positive three-digit number that is div in the Problem Solving forum “One approach is to check each answer choice, beginning with the largest answer choice E. 840 840 is divisible by 2, 3, 4, 5, 6 and 7 Answer: E Cheers, Brent” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the largest digit n for which the number 123,45n is in the Problem Solving forum “RULE: if the SUM of the digits of a number is divisible by 3, then that number is divisible by 3 Take, for example, the number 1,001,226 1 + 0 + 0 + 1 + 2 + 2 + 6 = 12 Since 12 is divisible by 3, we know that 1,001,226 is divisible by 3 If 123,45n is divisible by 3, then 1 + 2 + 3 + 4 + 5 + n ...” February 21, 2019 fskilnik@GMATH posted a new topic called The graphs of the functions f and g are represented in In th in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.ibb.co/3TSJ3Sf/21-Feb19-3z.gif The graphs of the functions f and g are represented in In the figure given. If f(x) = c^x (c constant), what is the value of g(g(-1)+1) + f(g(3)+1)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Answer: ____(E)__” February 21, 2019 Brent@GMATPrepNow posted a reply to In the figure above, the angle marked at c has been created in the Data Sufficiency forum “Target question: What is the sum of a, b, and c? This is a good candidate for rephrasing the target question. Since angles on a line add to 180°, we already know that b + c = 180 We get: a + b + c = a + 180 So, in order to find the sum of a, b and c, we need only find the value of a ...” February 21, 2019 GMATGuruNY posted a reply to In the figure above, the angle marked at c has been created in the Data Sufficiency forum “Since b and c form a straight line, b+c = 180. Thus, the calculate a+b+c, we need to know the value of a. Question stem, rephrased: What is the value of a? Statement 1: SUFFICIENT. Statement 2: No information about a. INSUFFICIENT. The correct answer is A.” February 21, 2019 Brent@GMATPrepNow posted a reply to At a certain committee meeting only associate professors and in the Problem Solving forum “Notice that the question asks us to find that TOTAL number of people present. In other words, it the question does NOT ask us to find the number of associate professors or assistant professors present. Since each person brings THREE items, and since total of 21 items were brought (10 pencils ...” February 21, 2019 GMATGuruNY posted a reply to At a certain committee meeting only associate professors and in the Problem Solving forum “Total number of items brought to the meeting = 21. (10 charts and 11 pencils) Number of items brought by each person = 3. (Either 2 pencils and 1 chart or 1 pencil and 2 charts) Thus: Number of people = (total number of items)/(number of items per person) = 21/3 = 7. The correct answer is B.” February 21, 2019 Brent@GMATPrepNow posted a reply to In a class of 30 students, 2 students did not borrow any in the Problem Solving forum “The average (arithmetic mean) number of book borrowed per student was 2. Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60 2 students borrowed 0 books: total of 0 books 12 students borrowed 1 book each: total of 12 books 10 students borrowed 2 books ...” February 21, 2019 Brent@GMATPrepNow posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “Target question: Is each of the numbers n the list equal to zero? Given: There are more than 2 numbers in the list Statement 1: The product of any 2 numbers in the list is ZERO There are several possible sets that satisfy this condition. Here are two: Case a: the set is {0, 0, 0} in ...” February 21, 2019 fskilnik@GMATH posted a reply to A box has only pure material A identical coins, pure materia in the Data Sufficiency forum “$$\left. \matrix{ {\rm{A}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{A}}\,\,\, \to \,\,\,\$x\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr {\rm{B}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{B}}\,\,\, \to \,\,\,\$ y\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr ...”
February 20, 2019
fskilnik@GMATH posted a reply to What is the value of the positive two-digit integer N? in the Data Sufficiency forum
“$$? = N = \left\langle {ab} \right\rangle \,\,\,\,\,\,\,\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio. P.S.: we know 28 and 39 could be found by some "organized manual work"... but the importance of the solution is contained in the ...” February 20, 2019 fskilnik@GMATH posted a reply to A number is called "mystic" if it can be expressed in the Problem Solving forum “$$?\,\,\,:\,\,\,M + \left( {M + 1} \right) + \left( {M + 2} \right) + \ldots + NM \ge 2N > 2M\,\,\,\,\,\leftYES, this is a very hard problem, but I believe many "pieces" of this solution are VERY useful for candidates aiming really outstanding performances! We follow ...”
February 20, 2019
fskilnik@GMATH posted a reply to Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“$$\left\{ { - 2, - 1,1,2} \right\}\,\, \to \,\,{\rm{two}}\,{\rm{different}}\,\,{\rm{chosen}}$$ $$? = P\left( {{\rm{odd}}\,\,{\rm{or}}\,\,{\rm{negative}}\,\,{\rm{product}}} \right)$$ $${\rm{6}}\,\,{\rm{equiprobable}}\,\,{\rm{outcomes}}\,\,:\,\,\,\left\{ \matrix{ \,\left\{ { - 2, - 1} ...” February 20, 2019 fskilnik@GMATH posted a reply to The product of three different numbers is greater than 1000. in the Data Sufficiency forum “$$a < b < cabc > 1000? = c\left( 1 \right)\,\,{\rm{primes}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\,\leftGMATH method. Regards, Fabio.”
February 20, 2019
fskilnik@GMATH posted a reply to Each student in a certain class is considered intermediate o in the Problem Solving forum
“https://i.ibb.co/MnVZF7c/19-Feb19-6j.gif $$?\,\, = \,\,\frac{{100}}{{100 + x}}$$ $$\left( {{\text{Alligation}}} \right)\,\,\,\,?\,\, = \,\,\frac{{100}}{{100 + x}}\,\, = \,\,\frac{{5.8 - 4.3}}{{6.3 - 4.3}}\,\, = \,\,\frac{{1.5}}{2}\,\, = \,\,\underleftrightarrow {\frac{1}{{10}}\left( ...” February 20, 2019 fskilnik@GMATH posted a reply to The graphs of y=7x+1 and y=kx^3 are represented in the figur in the Problem Solving forum “https://i.ibb.co/D8FnRQp/19-Feb19-5w.gif$$? = mC = \left( {c,8} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = 7 \cdot c + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 1C = \left( {c,8} \right) = \left( {1,8} \right) \in {\rm{cubic}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = k \cdot ...”
February 20, 2019
fskilnik@GMATH posted a new topic called A box has only pure material A identical coins, pure materia in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) A box has only pure material A identical coins, pure material B identical coins, and pure material C identical coins. Each coin is worth a certain integral number of dollars and coins of different materials don´t have the same dollar value. What is the ...”
February 20, 2019
GMATGuruNY posted a reply to Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“The following cases are possible: (-1)(1) = -1 (-1)(-2) = 2 (-1)(2) = -2 (1)(-2) = -2 (1)(2) = 2 (-2)(2) = -4 Of the 6 cases above, the 4 in blue each yield a product that is negative, odd or both: 4/6 = 2/3 ≈ 67%. The correct answer is D.”
February 20, 2019
Brent@GMATPrepNow posted a reply to Is mn < 10? in the Data Sufficiency forum
“Target question: Is mn < 10? Statement 1: m < 5 and n < 2 Let''s TEST some values. There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 0 and n = 0. In this case mn = (0)(0) = 0. So, the answer to the target question is YES, mn IS less than 10 ...”
February 20, 2019
fskilnik@GMATH posted a new topic called Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“GMATH practice exercise (Quant Class 19) Four cards are chosen from a standard deck: two aces (one of Spades, another of Hearts) and two kings (one of Spades, another of Hearts). The aces are considered as -1 (Spades) and 1 (Hearts), while the kings are considered as -2 (Spades) and 2 (Hearts). ...”
February 20, 2019
fskilnik@GMATH posted a new topic called What is the value of the positive two-digit integer N? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) What is the value of the positive two-digit integer N? (1) N and the product of the digits of N are 12 units apart. (2) N is greater than the product of the digits of N. Answer: ____(E)__”
February 20, 2019
fskilnik@GMATH posted a new topic called The product of three different numbers is greater than 1000. in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) The product of three different numbers is greater than 1000. What is the value of the largest among them? (1) The numbers are primes. (2) The product of the numbers is less than 1310. Answer: ___(E)__”
February 20, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #4: GMAT Data Sufficiency Strategies - Part I Video : https://www.youtube.com/watch?v=Ep09hi1OJpI Cheers, Brent”
February 20, 2019
Brent@GMATPrepNow posted a reply to John takes 15 hours to complete a certain job, while Bill ta in the Problem Solving forum
“Let''s first see what happens if Steven works as fast as possible. Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours. For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job. Unfortunately, ...”
February 20, 2019
Brent@GMATPrepNow posted a reply to If x, y, and z are three-digit positive integers and if x = in the Data Sufficiency forum
“Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. ...”
February 20, 2019
fskilnik@GMATH posted a reply to A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum
“$$? = 4L$$ $${L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” February 20, 2019 fskilnik@GMATH posted a reply to A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum “$$? = 4L{L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio.”
February 20, 2019
fskilnik@GMATH posted a new topic called Each student in a certain class is considered intermediate o in the Problem Solving forum
“GMATH practice exercise (Quant Class 6) Each student in a certain class is considered intermediate or strong, but not both. The average of the grades of the strong students is 6.3 points, exactly two points above the average of the grades of the intermediate students. What is the percentage of ...”
February 19, 2019
fskilnik@GMATH posted a new topic called A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum
“GMATH practice exercise (Quant Class 12) A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals? (A) ___(D)__”
February 19, 2019
fskilnik@GMATH posted a new topic called The graphs of y=7x+1 and y=kx^3 are represented in the figur in the Problem Solving forum
“GMATH practice exercise (Quant Class 13) https://i.ibb.co/f4YTfhw/19-Feb19-3w.gif The graphs of y=7x+1 and y=kx^3 are represented in the figure shown (k is a constant). If line AB is parallel to the x-axis, what is the abscissa (x-coordinate) of point B? (A) 1 (B) 0.75 (C) 0.5 (D) 0.25 ...”
February 19, 2019
fskilnik@GMATH posted a reply to Three points are randomly chosen on the circumference of a g in the Problem Solving forum
“We will refer to the link given in the hint: https://www.beatthegmat.com/three-points-are-chosen-independently-an-at-random-on-the-ci-t306462.html#826897 https://i.ibb.co/5nBHyTN/18-Feb19-5z.gif FOCUS: P(center inside the triangle) We may consider (without loss of generality) that the ...”
February 19, 2019
fskilnik@GMATH posted a reply to Is the x-intercept of the non-horizontal line L negative? in the Data Sufficiency forum
“$$c = {\left( {x - {\rm{intercept}}} \right)_{\rm{L}}}\,\,\mathop {\rm{ < }}\limits^? \,\,{\rm{0}}$$ $$L\,\,\,:\,\,\,{\rm{vertical}}\,\,{\rm{or}}\,\,{\rm{non - vertical}}\,\,{\rm{with}}\,\,m = {\rm{slop}}{{\rm{e}}_{\rm{L}}} \ne 0$$ $$\left( 1 \right)\,\,\,L\,\,{\rm{non - ...” February 19, 2019 Brent@GMATPrepNow posted a reply to George bought a large electronic item with a 15% off coupon in the Problem Solving forum “George was SUPPOSED to receive a 15% discount, but he received a 30% discount. So, he should have returned 15% of the original cost. However, the manager asked for half that amount (i.e., 7.5% of the original cost) In other words, 7.5% of the original cost = 40.50 IMPORTANT: at this point, ...” February 19, 2019 fskilnik@GMATH posted a new topic called A number is called \"mystic\" if it can be expressed as the su in the Problem Solving forum “GMATH practice exercise (Quant Class 17) A number is called "mystic" if it can be expressed as the sum of at least three consecutive positive integers greater than 1, in which the larger addend is more than twice the smaller addend. Note that 25 (=3+4+5+6+7) and 44 (=2+3+4+5+6+7+8+9) ...” February 19, 2019 fskilnik@GMATH posted a reply to If M, N are integers greater than 1 such that 2M<N, which in the Problem Solving forum “Although the problem seems hard, the focused-numbers (half the numbers given) are SMALL... and that´s the hint to try some "organized manual work"! We are looking for the 25 (III), 26 (II) and 27 (I) possibilities.$${S_K} = 1 + 2 + \ldots + K = {{K\left( {K + 1} \right)} \over ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Is x-y+1 greater than x+y-1 ? in the Data Sufficiency forum
“Target question: Is x - y + 1 > x + y - 1 ? This is a good candidate for rephrasing the target question. Take: x - y + 1 > x + y - 1 Subtract x from both sides to get: -y + 1 > y - 1 Add y to both sides to get: 1 > 2y - 1 Add 1 to both sides to get: 2 > 2y Divide both ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Anna has to visit at least 2 European cities on her vacation in the Problem Solving forum
“We need to consider 3 different cases: i) Anna visits 2 cities ii) Anna visits 3 cities iii) Anna visits 4 cities i) Anna visits 2 cities There are 4 options for the FIRST city and 3 options for the SECOND city So, the total number of 2-city itineraries = (4)(3) = 12 ii) Anna visits 3 ...”
February 19, 2019
Brent@GMATPrepNow posted a reply to Which of the following points is the intersection between in the Problem Solving forum
“KEY CONCEPT: The point of intersection (call P) of the lines y = 3x + 6 and y = -2x - 4 will be such that the x- and y-coordinates of P will satisfy BOTH equations. Since both equations are set equal to y, we can write: 3x + 6 = -2x - 4 Add 2x to both sides: 5x + 6 = - 4 Subtract 6 from both ...”
February 19, 2019
GMATGuruNY posted a reply to A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 in the Problem Solving forum
“Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 7 of the same color: 1 red 3 green 5 yellow 6 blue 6 white 6 black Sum = 1+3+5+6+6+6 = 27. Implication: It is possible to remove 27 balls without selecting 7 of the same ...”
February 19, 2019
fskilnik@GMATH posted a reply to How many positive perfect cubes are divisors of 4^6? in the Problem Solving forum
“Thank you for your nice contribution, Brent! $$?\,\,\,:\,\,\,\# \,\,{M^3}\,\,\,\left( {M \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,{{{4^6}} \over {{M^3}}}\,\,\mathop = \limits^{\left( * \right)} \,\,{\mathop{\rm int}}$$ $${4^6} = {2^{12}} = {\left( {{2^4}} ...” February 19, 2019 GMATGuruNY posted a reply to If M, N are integers greater than 1 such that 2M<N, which in the Problem Solving forum “54, 52 and 50 are options for TWICE the sum. Thus, I, II, and III imply the following options for the ACTUAL SUM: I: 27 II: 26 III: 25 Case 1: M=2 Since it is required that N>2M, N≥5 M=2 and N=5 --> sum = 2+3+4+5 = 14 M=2 and N=6 --> sum increases by 6 --> 14+6 = 20 M=2 and ...” February 19, 2019 fskilnik@GMATH posted a reply to In the second-degree equation x^2-14x+m = 0 the constant m in the Data Sufficiency forum “$${x^2} - 14x + m = 0\,\,,\,\,\,m \ge 1\,\,{\mathop{\rm int}} ? = B - A\,\,\,\,\left( {A < B\,\,{\rm{roots}}} \right)\,\,\left( * \right)\left( 1 \right)\,\,{\rm{equation}}\,\,{\rm{known}}\,\,\,\,\, \Rightarrow ...”
February 19, 2019
fskilnik@GMATH posted a reply to If A and B are two fixed constants such that the system in the Problem Solving forum
“Mitch´s nice solution is based on the fact that (A and B already fixed,) the solution sets of ordered pairs (x,y) that satisfy each equation alone represent (each one) a line in the rectangular coordinate system. We have two lines in the plane, hence they are concurrent (just one point (x,y) in ...”
February 19, 2019
GMATGuruNY posted a reply to If A and B are two fixed constants such that the system in the Problem Solving forum
“The system will have an infinite number of solutions for (x, y) if the two equations are THE SAME: 2(x+y) - A = 0 --> 2x + 2y - A = 0 --> 6x + 6y - 3A = 0 3x + By - 6 = 0 -----------------------> 6x +2By - 12 = 0 The equations in blue will be the same if 3A=12 and 2B=6, with the result ...”
February 18, 2019
fskilnik@GMATH posted a new topic called If A and B are two fixed constants such that the system in the Problem Solving forum
“GMATH practice exercise (Quant Class 2) Click on the image to open it in a much larger version! https://i.ibb.co/6nhYNZy/18-Feb19-7x.gif Answer: ____(B)__”
February 18, 2019
fskilnik@GMATH posted a new topic called Three points are randomly chosen on the circumference of a g in the Problem Solving forum
“GMATH practice exercise (Quant Class 19) Three points are randomly chosen on the circumference of a given circle. What is the probability that the center of the circle lies inside the triangle whose vertices are at the three points? (A) 1/3 (B) 1/4 (C) 1/5 (D) 2/5 (E) 2/7 Hint: the ...”
February 18, 2019
fskilnik@GMATH posted a new topic called Is the x-intercept of the non-horizontal line L negative? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 20) Is the x-intercept of the non-horizontal line L negative? (1) The slope of line L is equal to the y-intercept of line L. (2) The slope of line L is positive. Answer: ____(A)__”
February 18, 2019
fskilnik@GMATH posted a new topic called If M, N are integers greater than 1 such that 2M<N, which of in the Problem Solving forum
“GMATH practice exercise (Quant Class 17) If M, N are integers greater than 1 such that 2M < N, which of the following numbers could be twice the value of the sum of all integers from M to N, including both of them? I. 54 II. 52 III. 50 (A) I. only (B) II. only (C) III. only (D) ...”
February 18, 2019
Brent@GMATPrepNow posted a reply to How many positive perfect cubes are divisors of 4^6? in the Problem Solving forum
“4⁶ = (2²)⁶ = 2¹² Since 2¹² = (2³)(2⁹), we know 2³ is a divisor of 2¹² Since 2¹² = (2⁶)(2⁶), we know 2⁶ is a divisor of 2¹² Since 2¹² = (2⁹)(2³), we know 2⁹ is a divisor of 2¹² Since 2¹² = (2¹²)(2⁰), we know 2¹² is a divisor of 2¹² Since 2¹² = ...”
February 18, 2019
Brent@GMATPrepNow posted a reply to The squares of two consecutive positive integers differ by 5 in the Problem Solving forum
“Let x = the smaller integer So, x+1 = the larger integer (since the numbers are CONSECUTIVE) The squares of two consecutive positive integers differ by 55. We can write: (x + 1)² - x² = 55 Expand: x² + 2x + 1 - x² = 55 Simplify: 2x + 1 = 55 So: 2x = 54 Solve: x = 54/2 = 27 Answer: ...”
February 18, 2019
fskilnik@GMATH posted a new topic called In the second-degree equation x^2-14x+m = 0 the constant m in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) In the second-degree equation x^2-14x+m = 0, the constant m is a positive integer. If A < B are the roots of this equation, what is the value of B-A ? (1) m=33 (2) A and B are two primes Answer: ____(D)__”
February 18, 2019
fskilnik@GMATH posted a new topic called How many positive perfect cubes are divisors of 4^6? in the Problem Solving forum
“GMATH practice exercise (Quant Class 16) How many positive perfect cubes are divisors of 4^6 ? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Answer: _____(D)__”
February 18, 2019
GMATGuruNY posted a reply to Is m > n? in the Data Sufficiency forum
“Both statements are satisfied if n=1 and m=2 or if n=1 and m=-2. Since m > n in the first case but m < n in the second case, the two statements combined are INSUFFICIENT. The correct answer is E.”
February 18, 2019
GMATGuruNY posted a reply to If the original price of an item in a retail store is marked in the Data Sufficiency forum
“Let the original price = 100. Then the markup = (m/100)*100 = m. The resulting price = 100+m. The subsequent discount = d/100*(100+m) = d + md/100 Thus, the total percent change = percent increase - percent decrease = m - d - md/100. For the final price to be greater than the original price, ...”
February 17, 2019
GMATGuruNY posted a reply to In triangle ABC, point X is the midpoint of side AC and poin in the Data Sufficiency forum
“http://s7.postimage.org/6u5drpql3/triangle_RCS_1.jpg Triangles RCS and ABC: Side RC = 1/4(AC). Side SC = 1/4(BC). The two triangles share angle BCA. Triangles with a shared angle (BCA) formed by corresponding sides in the same proportion (RC:AC = 1:4, SC:BC = 1:4) are SIMILAR. Thus, ...”
February 17, 2019
GMATGuruNY posted a reply to A and B start from Opladen and Cologne respectively at the in the Problem Solving forum
“When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same. If A takes 1/2 as long as B to travel 10 miles, then A will take 1/2 as long as B to travel 1000 miles. If A takes 3 times as long as B to travel 500 miles, then A will take three ...”
February 17, 2019
GMATGuruNY posted a reply to Flor is choosing three of five colors of paint to use for in the Problem Solving forum
“Let the 5 colors be GYABC. From the 5 colors, the number of ways to choose 3 = 5C3 = (5*4*3)/(3*2*1) = 10. Of these 10 combinations, 3 are not allowed: GYA GYB GYC Subtracting these 3 bad combinations, we get: 10-3 = 7. The correct answer is A.”
February 17, 2019
Brent@GMATPrepNow posted a reply to A scientist has 400 units of a 6% phosphoric acid solution, in the Problem Solving forum
“We can solve this question with the weighted averages formula: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let x = the number of units of 12% phosphoric acid solution needed ...”
February 16, 2019
Brent@GMATPrepNow posted a reply to If a = 15! + 13, which of the following are factors of a? I in the Problem Solving forum
“Here''s a similar question to practice with: https://www.beatthegmat.com/divisibility-t111432.html Cheers, Brent”
February 16, 2019
Brent@GMATPrepNow posted a reply to Phone plan A charges $1.25 for the first minute and$0.15 in the Problem Solving forum
“Phone plan A charges $1.25 for the first minute and$0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call = $1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay$1.25 for the FIRST minute. So, if x = ...”
February 16, 2019
Brent@GMATPrepNow posted a reply to A magician has five animals in his magic hat: 3 doves and 2 in the Problem Solving forum
“Let''s apply probability rules First notice that, to get a matched pair, we can select 2 doves or 2 rabbits. So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove) We can now apply our AND and OR rules to get: P(matched pair) = x P(2nd ...”
February 16, 2019
GMATGuruNY posted a reply to If a = 15! + 13, which of the following are factors of a? I in the Problem Solving forum
“MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X. MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X. Since the prime-factorization of 15! includes 13, we get: a = 15! + 13 = multiple of 13 + multiple of 13 = multiple of 13. Since a is a multiple of 13, option I is a factor of a. Eliminate ...”
February 16, 2019
GMATGuruNY posted a reply to If a coin has an equal probability of landing heads up or ta in the Problem Solving forum
“P(H) = 1/2. P(T) = 1/2. One way to get exactly 1 heads in 3 flips: P(HTT) = 1/2 * 1/2 * 1/2 = 1/8. Since H can appear in a total of 3 positions -- 1st flip, 2nd flip, or 3rd flip -- we multiply by 3: 1/8 * 3 = 3/8 = 0.375. The correct answer is C.”
February 16, 2019
GMATGuruNY posted a reply to A magician has five animals in his magic hat: 3 doves and 2 in the Problem Solving forum
“AND means MULTIPLY. OR means ADD. Case 1: 2 doves P(1st animal is a dove) = 3/5. (Of the 5 animals, 3 are doves.) P(2nd animal is a dove) = 2/4. (Of the 4 remaining animals, 2 are doves.) Since in Case 1 we need the 1st animal to be a dove AND the 2nd animal to be a dove, we MULTIPLY the ...”
February 16, 2019
fskilnik@GMATH posted a reply to If a positive integer q is divisible by both 3 and 11, then in the Problem Solving forum
“$$q \ge 1\,\,{\mathop{\rm int}}$$ $${q \over 3} = {\mathop{\rm int}} \,\,\,;\,\,\,\,{q \over {11}} = {\mathop{\rm int}} \,\,\,\,\,\left( * \right)$$ $$?\,\,\,:\,\,\,{q \over {{\rm{altern}}}} = {\mathop{\rm int}}$$ $$\left. \matrix{ ...” February 15, 2019 Brent@GMATPrepNow posted a reply to If a positive integer q is divisible by both 3 and 11, then in the Problem Solving forum “I. 14 14 is NOT divisible by 3 or 11 So, statement I is NOT true. ELIMINATE A and D III. 66 Integer q COULD equal 33 (which is divisible by 3 and 11) Since 33 is NOT divisible by 66, statement III is NOT true. ELIMINATE C and E By the process of elimination, the correct answer is B ...” February 15, 2019 Brent@GMATPrepNow posted a reply to Kevin buys beer in bottles and cans. He pays 1.00 for each in the Data Sufficiency forum “Target question: How many bottles of beer did Kevin buy? Given: Kevin pays 1.00 for each can of beer and 1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can ...” February 15, 2019 fskilnik@GMATH posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “LoL... I was only joking, but I thank you for that. You are not only an excellent teacher/professional... you are a gentleman! Have a great weekend! Regards, Fabio.” February 15, 2019 GMATGuruNY posted a reply to What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{20 in the Problem Solving forum “(2²⁰²⁰ + 2²⁰¹⁸)/(2²⁰²⁰ - 2²⁰¹⁸) = (2²⁰¹⁸)(2² + 1) / (2²⁰¹⁸)(2² - 1) = 5/3. The correct answer is B.” February 15, 2019 GMATGuruNY posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “In deference to your mother, the offensive second "c" has been removed from my solution.” February 15, 2019 GMATGuruNY posted a reply to A certain military vehicle can run on pure Fuel X, pure Fuel in the Data Sufficiency forum “Statement 1: X = 20 miles per gallon. Y = 40 miles per gallon. Since the mixture of X and Y in the tank allows 200 miles to be covered using 8 gallons, we get: X+Y = 200/8 = 25 miles per gallon. To determine how X and Y must be combined to yield a rate of 25 miles per gallon, use ALLIGATION. ...” February 15, 2019 fskilnik@GMATH posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “Hi Mitch! Thanks for joining. We all know that Data Sufficiency is related to the uniqueness (and viability) of potential answers, but "easier math" is a nice contribution. Just one important detail. Rebeca (my mother!) has only one "c", please... ;) Regards, ...” February 15, 2019 GMATGuruNY posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “To make the math easier, we can replace the given values with rounder numbers, as follows: Since Rebeca arrives 1 hour late when traveling at the lower speed and 1 hour early when traveling at the higher speed, the time at the lower speed must be 2 hours greater than the time at the higher ...” February 15, 2019 fskilnik@GMATH posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “$$?\,\, = \,\,d\,\,\,\,\left( {{\rm{miles}}} \right)\left. \matrix{ \left( {{\rm{late}}} \right)\,\,:\,\,\,d\,\,{\rm{miles}}\left( {{{60\,\,\min } \over {x\,\,{\rm{miles}}}}} \right)\,\,\, = \,\,\,{{60d} \over x}\,\,\min \,\,\, \hfill \cr \left( {{\rm{early}}} ...”
February 15, 2019
fskilnik@GMATH posted a reply to What is the value of a^3+b^3 ? in the Data Sufficiency forum
“$$? = {a^3} + {b^3}$$ $$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr \,{\rm{Take}}\,\left( {a,b} \right) = \left( {2, - 1} \right)\,\,\,\, \Rightarrow \,\,\,? \ne 1 \hfill \cr} \right.$$ ...”
February 15, 2019
fskilnik@GMATH posted a reply to If 4<=x<=6 and 2<=y<=3, then in the Problem Solving forum
“$$?\,\, = \,\,\min \,\left| {\left( {y - x} \right)\left( {y + x} \right)} \right|\,\, = \,\,\min \,\left| {{y^2} - {x^2}} \right|$$ \eqalign{ & 2 \le y \le 3\,\,\,\,\, \Rightarrow \,\,\,\,\,4 \le {y^2} \le 9 \cr & 4 \le x \le 6\,\,\,\,\, \Rightarrow \,\,\,\,\,16 \le {x^2} \le ...” February 15, 2019 fskilnik@GMATH posted a reply to Which of the following numbers is closest to 100*(11-sqrt( in the Problem Solving forum “?\,\,\,:\,\,\,\,100\left( {11 - \sqrt {119} } \right)\,\,\,{\rm{approx}}{\rm{.}}\left( {11 - \sqrt {119} } \right)\left( {11 + \sqrt {119} } \right) = {11^2} - 119 = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,11 - \sqrt {119} = {2 \over {11 + \sqrt {119} }}100 < 119 < 121\,\,\,\, ...”
February 15, 2019
fskilnik@GMATH posted a reply to Three points are chosen independently an at random on the ci in the Problem Solving forum
“https://i.ibb.co/HChP16b/14-Feb19-10w.gif Very nice problem! FOCUS : the probability of having all three points chosen (say blue, red and green, in that order) "sufficiently close". 1. The first point (blue) may be considered (without loss of generality) placed at the top of the ...”
February 15, 2019
GMATGuruNY posted a reply to Which of the following numbers is closest to 100*(11-sqrt( in the Problem Solving forum
“100(11 - √119)(11 + √119) = 100(11² - √119²) = 100(121-119) = 100*2 = 200. When the correct answer is multiplied by 11+√119, the result must be as close as possible to 200. 11+√119 = 11 + (a bit less than 11) = a bit less than 22. Since 9*22 = 198, multiplying 9.2 by a bit less than ...”
February 14, 2019
GMATGuruNY posted a reply to What is the value of a^3+b^3 ? in the Data Sufficiency forum
“Statement 1: Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1 In this case, a³+b³ = 0³ + 1³ = 1 Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1 In this case, a³+b³ = 2³ + (-1)³ = 7 Since a³+b³ can be different values, INSUFFICIENT. Statement 2: Case 3: a=1 and b=1, ...”
February 14, 2019
fskilnik@GMATH posted a new topic called Which of the following numbers is closest to 100*(11-sqrt( in the Problem Solving forum
“GMATH practice exercise (Quant Class 12) https://i.ibb.co/f1Rk8yt/14-Feb19-9x.gif Answer: ____(B)__”
February 14, 2019
fskilnik@GMATH posted a new topic called What is the value of a^3+b^3 ? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) https://i.ibb.co/Lxkfrgg/14-Feb19-8v.gif Answer: ____ (C)__ ”
February 14, 2019
fskilnik@GMATH posted a new topic called If 4<=x<=6 and 2<=y<=3, then in the Problem Solving forum
February 14, 2019
GMATGuruNY posted a reply to A group of x people is practicing levitation yoga. One-fourt in the Problem Solving forum
“Let x=12. Since 1/4 of the people rise up, the number who rise up = (1/4)(12) = 3. Since 3 people come back down, EVERYONE who rises up comes back down, with the result that all 12 people are practicing yoga on the ground. How many people are now practicing yoga on the ground? The correct ...”
February 14, 2019
fskilnik@GMATH posted a reply to Is |a|<1? in the Data Sufficiency forum
“$$\left| a \right|\,\,\mathop < \limits^? \,\,1$$ $$\left( 1 \right)\,\,{a^2} < 1\,\,\, \Rightarrow \,\,\,\sqrt {{a^2}} < \sqrt 1 \,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ $$\left( 2 \right)\,\,{1 \over {1 - {a^2}}} > 0\,\,\,\, \Rightarrow \,\,\,\,1 - ...” February 14, 2019 Brent@GMATPrepNow posted a reply to A group of x people is practicing levitation yoga. One-fourt in the Problem Solving forum “ One-fourth of the people rise up in the air If 1/4 of the x people are in the AIR, the remaining 3/4 of the x people are on the GROUND So, (3/4)x = number of people on the GROUND After a while, 3 of them come back down. So, the number of people on the GROUND is increased by 3 So, now ...” February 14, 2019 Brent@GMATPrepNow posted a reply to In the figure above, polygon N has been partially covered by in the Data Sufficiency forum “Target question: How many sides does N have? Statement 1: x + y = 45 Since all angles in a triangle add to 180°, we know that the missing angle is 135° https://i.imgur.com/oUCDRTN.png There are plenty of polygons that have at least one angle measuring 135°. Here are two: Case a: ...” February 14, 2019 Brent@GMATPrepNow posted a reply to Which of the following expressions is equal to 2^32-2^31-2^3 in the Problem Solving forum “2^32 - 2^31 - 2^30 = (2^30)(2^2 - 2^1 - 1) = (2^30)(4 - 2 - 1) = (2^30)(1) = 2^30 Answer: C Cheers, Brent” February 14, 2019 fskilnik@GMATH posted a new topic called If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum “GMATH practice exercise (Quant Class 19) If Rebeca drives to work at x mph she will be one minute late, but if she drives at y mph she will be one minute early. How far (in miles) does Rebeca drive to work? (1) x and y differ by seven miles per hour. (2) y is 11% greater than x. ...” February 14, 2019 fskilnik@GMATH posted a reply to If x^(1-x) = 4, what is the value of in the Problem Solving forum “$${x^{1 - x}} = 4\,\,\,\,\, \Rightarrow \,\,\,\,\,{x^{ - \left( {1 - x} \right)}} = {4^{ - 1}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{x^{x - 1}} = {1 \over 4}\,\,\,\,\,\,\,\left( * \right)?\,\, = \,\,{x^{{x^x}\,\, - \,\,{{{x^x}} \over x}}}\,\, = \,\,{x^A}\,\,\,\,\,\,\,\,\,\,\,\,\left( {A = {x^x}\,\, ...”
February 14, 2019
fskilnik@GMATH posted a reply to If ABCD is a rectangle, what is the value of y+z in the Data Sufficiency forum
“Obs.: all angles are measured in degrees. https://i.ibb.co/LS7VNBC/14-Feb19-4j.gif $$\left( {{\rm{Vertex}}\,A\,,\,\,{\rm{see}}\,\,{\rm{first}}\,\,{\rm{figure}}} \right)\,\,\,\,\,\left( {90 - y} \right) + x + \left( {90 - z} \right) = 90\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y + z = x + ...” February 14, 2019 fskilnik@GMATH posted a reply to In the rectangular coordinate system, which of the above rep in the Problem Solving forum “$${\rm{?}}\,\,\,{\rm{:}}\,\,\,{\rm{best}}\,\,{\rm{graph}}\,\,{\rm{representation}}{y \over {x - y}}\,\,\mathop > \limits^{\left( * \right)} \,\,0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,y > 0\,\,\,{\rm{and}}\,\,\,x - y > 0 \hfill \cr \,\,\,{\rm{OR}} \hfill ...”
February 14, 2019
fskilnik@GMATH posted a new topic called If x^(1-x) = 4, what is the value of in the Problem Solving forum
February 14, 2019
fskilnik@GMATH posted a new topic called If ABCD is a rectangle, what is the value of y+z in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 15) https://i.ibb.co/R7DgtQN/13-Feb19-7r.gif If ABCD is a rectangle, what is the value of y+z ? (1) x = 40 (2) M is the midpoint of line segment BC, and N is the midpoint of line segment CD Answer: ____(A)__”
February 14, 2019
fskilnik@GMATH posted a new topic called In the rectangular coordinate system, which of the above rep in the Problem Solving forum
“GMATH practice exercise (Quant Class 20) https://i.ibb.co/5GK37Kd/13-Feb19-3c.gif In the rectangular coordinate system, which of the above representations better describes the points (x,y) such that y/(x-y) > 0? (Alternative choices are presented in the figure.) Answer: ...”
February 13, 2019
Brent@GMATPrepNow posted a reply to OG L-shaped garden in the Data Sufficiency forum
“Target question: What is the value of k? Statement 1: The area of the garden is 189 square feet. Let''s drawn an auxiliary line that divides the shape into two rectangular regions A and B. https://i.imgur.com/hJBOxsO.png Regions A and B have the following measurements. ...”
February 13, 2019
Brent@GMATPrepNow posted a reply to How many integers between 18 and 3399 are multiples of 17? in the Problem Solving forum
“Let''s list the multiples of 17 that are between 18 and 3399 : 34 = 2(17) 51 = 3(17) 68 = 4(17) 85 = 5(17) . . . 3383 = 199(17) So, the number of multiples of 17 is EQUAL to the number of integers from 2 to 199 inclusive ASIDE: A nice rule says: the number of integers from x to y ...”
February 13, 2019
fskilnik@GMATH posted a reply to Triangle ABC is equilateral and inscribed in the circle with in the Data Sufficiency forum
“https://i.ibb.co/yXx67Pw/12-Feb19-6u.gif $$? = {S_{\Delta APQ}}$$ (1) Clearly insufficient, as PROVED by the algebraic-geometric bifurcation (figure, first row): > In the figure on the left, we have chosen P sufficiently close to B such that our focus is "as near as desired" to ...”
February 13, 2019
Brent@GMATPrepNow posted a reply to A mountain resort will hold its annual one-day snowboarding in the Problem Solving forum
“GIVEN: P(snow) = 0.7, so P(no snow) = 0.3 Let''s use the complement to solve this. That is, P(event is held) = 1 - P(event is NOT held) P(event is NOT held) = P(no snow on Saturday AND no snow on Sunday) = P(no snow on Saturday) x P(no snow on Sunday) = 0.3 x 0.3 = 0.09 So, P(event is ...”
February 13, 2019
GMATGuruNY posted a reply to How many prime factors does the number X have? 1) X is divi in the Data Sufficiency forum
“Statement combined: Case 1: X = 53*2 = 106, with the result that X is divisible by 1, 2, 53, and 106 In this case, X has TWO prime factors: 2 and 53 Case 2: X = 53³, with the result that X is divisible by 1, 53, 53², and 53³ In this case, X has only ONE prime factor: 53 Since the number of ...”
February 13, 2019
fskilnik@GMATH posted a reply to A positive 5-digit integer is called "friendly" if in the Problem Solving forum
“ FOCUS: the units digit of the 32nd friendly number 1. The first P4 = 4! = 24 friendly numbers "start with 1" (i.e., 1 _ _ _ _ ) , the (few) next ones "start with 2". 2. "Starting with 2" (i.e., 2 _ _ _ _ ), there are P3 = 3! = 6 friendly numbers ...”
February 13, 2019
fskilnik@GMATH posted a reply to Winston created a function F such that F(1)=4, F(4)=3 and F( in the Problem Solving forum
“$$F\left( {F\left( x \right)} \right) = F\left( {x + 2} \right) - 3\,\,\,,\,\,\,x\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right)$$ $$F\left( 1 \right) = 4\,\,,\,\,F\left( 4 \right) = 3\,\,\,\,\,\left( {**} \right)$$ $$? = F\left( 5 \right)$$ $$x = 3\,\,\,\,\mathop \Rightarrow \limits^{\left( ...” February 13, 2019 Brent@GMATPrepNow posted a reply to The product P of two prime numbers is between 9 and 55. in the Problem Solving forum “Prime numbers that are greater than 2 but less than 6: 3, 5 Prime numbers that are greater than 13 but less than 25: 17, 19, 23 Scan the answer choices . . . E) 51 = 3 x 17 PERFECT! Answer: E Cheers, Brent” February 12, 2019 GMATGuruNY posted a reply to A terminating decimal is a number with a finite number of in the Data Sufficiency forum “A fraction will yield a terminating decimal if -- when the fraction is fully reduced -- the prime-factorization of its denominator includes only 2''s and or 5''s. Statement 1: Let x = an odd multiple of 5. Since the next largest odd multiples of 5 will be x+10 and x+20, we get: p = x + (x+10) ...” February 12, 2019 GMATGuruNY posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum “A radius drawn to a tangent point yields a RIGHT ANGLE: https://i.postimg.cc/Wq6BDNH7/two-triangles-and-semicircle-1.png In the figure above: Radius OT forms a right angle at tangent point T. OA and OT are radii and thus are equal. Since OA=OT, opposite angles OAT and ATO are equal. We can ...” February 12, 2019 fskilnik@GMATH posted a new topic called Winston created a function F such that F(1)=4, F(4)=3 and F( in the Problem Solving forum “GMATH practice exercise (Quant Class 4) Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x+2)-3, for all integer values of x. What is the value of F(5)? (A) 0 (B) 2 (C) 4 (D) 12 (E) Not necessarily one above Answer: ____(D)__” February 12, 2019 fskilnik@GMATH posted a reply to What is the probability that you get a pair when picking the in the Problem Solving forum “$$?\,\, = \,\,P\left( {{\rm{get}}\,\,{\rm{a}}\,\,{\rm{pair}}} \right)\left. \matrix{ {\rm{Total}}\,\,:\,\,\,C\left( {52,2} \right) = {{52 \cdot 51} \over 2} = 26 \cdot 51\,\,\,{\rm{equiprobable}}\,\,{\rm{choices}}{\kern 1pt} \,\, \hfill \cr {\rm{Favorable}}\,\,:\,\,\,\underbrace ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to What is the probability that you get a pair when picking the in the Problem Solving forum
“P(select pair) = P(1st card is ANY card AND 2nd card matches 1st card) = P(1st card is ANY card) x P(2nd card matches 1st card) = 1 x 3/51 = 3/51 = 1/17 = C Aside: P(2nd card matches 1st card) = 3/51, because once 1 card is selected, there are 51 cards remaining in the deck. Among those 51 ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to At her current job, Mary gets a 1.5% raise twice per year. in the Problem Solving forum
“One approach here is to apply the COMPOUND INTEREST formula. However, if you didn''t see that the question is analogous to a COMPOUND INTEREST question, we can also solve the question by looking for a pattern. Let''s try that: Time elapsed (in years) | salary 0 | s 0.5 | (1.015)(s) 1 | ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to Of the 3,000 cars manufactured in Factory Q last year, how in the Data Sufficiency forum
“Target question: Of the 3,000 cars manufactured in Factory Q LAST YEAR, how many were still in operation at the end of the year? Neither statement provides any information about the cars manufactured LAST YEAR. Instead, we''re told about ALL of the cars ever manufactured . As such, the ...”
February 12, 2019
GMATGuruNY posted a reply to A positive 5-digit integer is called "friendly" if in the Problem Solving forum
“Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120. There are 5 options for the first digit: 1, 2, 3, 4, or 5. 120/5 = 24. Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows: The integers beginning with 1 constitute friendly ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to In the figure given, x = 3(y-z). What is the value of x? in the Problem Solving forum
“Since angles on a LINE add to 180°, . . . https://i.imgur.com/kAdhC7N.png . . . we know that x + z = 180 Subtract x from both sides to get: z = 180 - x Since angles in a CIRCLE add to 360°. . . https://i.imgur.com/l1SKqw5.png . . . we know that 60 + (180 - x) + y = 360 Simplify left ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to In the xy-coordinate plane, if the point (0,2) lies on the g in the Problem Solving forum
“KEY CONCEPT: In order for a point to be ON a line, the x- and y-coordinates of the point must satisfy the equation of that line So, for example, the point (3,7) lies ON the line defined by the equation y = 2x + 1, because x = 3 and y = 7 satisfy the equation y = 2x + 1 That is, 7 = 2(3) + 1 ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to Set S consists of n consecutive integers, where n > 1. in the Data Sufficiency forum
“ Given: Set S consists of n consecutive integers, where n > 1. Target question: What is the value of n? IMPORTANT: Notice that the two statements are VERY SIMILAR. That is, if the sum of the values is 14 (statement 2), then it is guaranteed that the sum is divisible by 7 (statement 1). ...”
February 12, 2019
fskilnik@GMATH posted a new topic called A positive 5-digit integer is called \"friendly\" if each of i in the Problem Solving forum
“GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: ...”
February 12, 2019
fskilnik@GMATH posted a new topic called Triangle ABC is equilateral and inscribed in the circle with in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 15) https://i.ibb.co/KGBvb6T/12-Feb19-4m.gif Triangle ABC is equilateral and inscribed in the circle with center O. What is the value of the shaded area? (1) The length of the radius of the circle is 2 (2) Lines PQ and BC are parallel Answer: ...”
February 12, 2019
fskilnik@GMATH posted a reply to In the figure given, x = 3(y-z). What is the value of x? in the Problem Solving forum
“Obs.: all angles are measured in degrees. https://i.ibb.co/3NN9sRn/07-Feb19-5rt.gif $$x = 3\left( {y - z} \right)\,\,\,\,\,\left( * \right)$$ $$? = x$$ $$\left( {{\rm{Last}}\,\,{\rm{figure}}} \right)\,\,\,\,x + z = \leftThe correct answer is therefore (C). We follow the notations and ...” February 12, 2019 GMATGuruNY posted a reply to How many numbers between 1 and 200, inclusive, have a 2 in in the Problem Solving forum “An integer is divisible by 4 if its last two digits form a multiple of 4. Two-digit multiples of 4 with a units digit of 2: 12, 32, 52, 72, 92 Since the last two digits must be one of the options above, between 1 and 200 there are 10 integers that have a units digit of 2 and are divisible by 4: ...” February 12, 2019 GMATGuruNY posted a reply to If triangles ABC and CDE are each equilateral, what is the s in the Data Sufficiency forum “Statement 1: Case 1: AC = 10 and CE = 15, with the result that AE = 10+15 = 25 In this case, ABC + CDE = (10+10+10) + (15+15+15) = 75. Case 2: AC= 5 and CD = 20, with the result that AE = 5+20 = 25 In this case, ABC + CDE = (5+5+5) + (20+20+20) = 75. Since the sum of the perimeters is the same ...” February 12, 2019 GMATGuruNY posted a reply to If m is a positive odd integer, what is the average (arithme in the Data Sufficiency forum “For any EVENLY SPACED SET: average = median Statement 1: Here, the set consists of consecutive multiples of 3 and thus is evenly spaced. Case 1: 3, 6, 9 Average = median = 6. Case 2: 6, 9, 12 Average = median = 9. Since different averages are possible, INSUFFICIENT. Statement 2: Case ...” February 12, 2019 fskilnik@GMATH posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum “Hi, Brent! Thank you for your nice contribution and beautiful drawings! https://i.ibb.co/2F77Nbh/11-Feb19-5z.gif Alternate approach: (Click in the figure to "zoom" it! All angles are measured in degrees.)$$? = x\Delta BTC\,\,:\,\,\,3x + 2x = 90\,\,\,\,\,\, \Rightarrow ...”
February 12, 2019
fskilnik@GMATH posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum
“Post appeared twice. Please see my solution below!”
February 12, 2019
GMATGuruNY posted a reply to If there is a 20% chance of rain every day for the next 7 in the Problem Solving forum
“Options D and E should appear as shown below: P(exactly n times) = P(one way) * all possible ways. Let R = rain and N = no rain. Since P(R) = 20% = 2/10, P(N) = 80% = 8/10 = 2³/10. P(one way): One way to get exactly 2 days of rain is to have rain on the first 2 days but not on the ...”
February 12, 2019
Brent@GMATPrepNow posted a reply to A computer chip manufacturer expects the ratio of the number in the Problem Solving forum
“Let''s find some TOTALS for all 4 shipments combined. There are 51,000 chips altogether There are 17 defective chips altogether. So, 17/51000 of the chips are defective. (notice that 17 divides nicely into 51000!) SIMPLIFY: 1/3000 of the chips are defective So, if we have a shipment of ...”
February 11, 2019
Brent@GMATPrepNow posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum
“Since angles in a triangle add to 180°, we know that the missing angle = (90 - 2x)° https://i.imgur.com/FcSiZi2.png Aside: Notice that (90 - 2x)° + 90° + 2x° =180° Since angles on a line add to 180°, we know that the missing angle = (90 + 2x)° https://i.imgur.com/9Z5ULFo.png ...”
February 11, 2019
fskilnik@GMATH posted a new topic called If O is the center of the circle with diameter AB and T is a in the Problem Solving forum
“GMATH practice exercise (Quant Class 7) https://i.ibb.co/yqP84nM/11-Feb18-3z.gif If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 Answer: ____(C)__”
February 11, 2019
fskilnik@GMATH posted a reply to If m and n are integers greater than 1, what is the value of in the Data Sufficiency forum
“$$m\,,n\,\, \ge 2\,\,\,{\rm{ints}}\,\,\,\,\,\left( * \right)$$ $$?\,\, = \,\,A\left( {m,n} \right)\,\, = \,\,{{\root m \of {{2^n}} + \root n \of {{2^m}} } \over {{2^m} + {2^n}}}$$ $$\left( 1 \right)\,\,m = n\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} ...” February 11, 2019 Brent@GMATPrepNow posted a reply to tough geo. problem in the Data Sufficiency forum “Target question: What is the length of side BC? Statement 1: Line segment AD has length 6. BEFORE we deal with statement 1, let''s see what information we can add to the diagram. For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC: ...” February 11, 2019 fskilnik@GMATH posted a reply to What is the value of F(-1)-F(1) ? in the Data Sufficiency forum “$$? = F\left( { - 1} \right) - F\left( 1 \right)\left( 1 \right)\,\,F\left( x \right) = {x^2}\,,\,\,{\rm{for}}\,\,{\rm{all}}\,\,x\,\,\,\, \Rightarrow \,\,\,\,F\left( x \right) = F\left( { - x} \right)\,,\,\,{\rm{for}}\,\,{\rm{all}}\,\,x\,\,\,\,\mathop \Rightarrow \limits^{x\, = \,1} ...”
February 11, 2019
Brent@GMATPrepNow posted a reply to What is the area of a right triangle? in the Data Sufficiency forum
“Target question: What is the area of a right triangle? Statement 1: The length of one side is 3 Knowing the length of only 1 side will not help us answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: The length of one side is 4 NOT SUFFICIENT (same ...”
February 11, 2019
Brent@GMATPrepNow posted a reply to If x=0.2, then what is the value of x^3-1/x-1? in the Problem Solving forum
“Some spaces and/or brackets would definitely help here. Do you mean x^3 - 1/x - 1 or x^3 - 1/(x - 1) or (x^3 - 1)/(x - 1)?? Cheers, Brent”
February 11, 2019
fskilnik@GMATH posted a new topic called If O is the center of the circle with diameter AB and T is a in the Problem Solving forum
“GMATH practice exercise (Quant Class 1) https://i.ibb.co/gw4DXfW/11-Feb19-3m.gif In the figure given, x = 3(y-z). What is the value of x? (A) 27 (B) 33 (C) 36 (D) 45 (E) 72 Answer: ____(C)__”
February 11, 2019
Brent@GMATPrepNow posted a reply to If n and p are integers, is p > 0? in the Data Sufficiency forum
“ Given: n and p are integers Target question: Is p > 0? Statement 1: n + 1 > 0 No information about p. Statement 1 is NOT SUFFICIENT Statement 2: np > 0 There are several values of n and p that satisfy statement 2. Here are two: Case a: n = 1 and p = 1. In this case, ...”
February 11, 2019
fskilnik@GMATH posted a new topic called If m and n are integers greater than 1, what is the value of in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) If m and n are integers greater than 1, what is the value of A(m,n) ? $$A\left( {m,n} \right) = {{\root m \of {{2^n}} + \root n \of {{2^m}} } \over {{2^m} + {2^n}}}$$ $$\left( 1 \right)\,\,m = n$$ $$\left( 2 \right)\,\,m + n = m \cdot n$$ Answer: ...”
February 11, 2019
fskilnik@GMATH posted a new topic called What is the value of F(-1)-F(1) ? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) What is the value of F(-1)-F(1) ? (1) F(x) = x^2 , for all x (2) F(x+1) = F(x) + 2x + 1, for all x Answer: ____(D)__”
February 11, 2019
Brent@GMATPrepNow posted a reply to If x and y are integers, is x^2-y^2 odd? in the Data Sufficiency forum
“Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is x² - y² odd? IMPORTANT: Notice that we can factor x² - y² to get: x² - y² = (x + y)(x - y) ...”
February 10, 2019
Brent@GMATPrepNow posted a reply to In a group of 100 adults, 75 percent of the women are in the Problem Solving forum
“GIVEN: 75% women are LEFT handed This also tells us that 25% women are RIGHT handed GIVEN: There are 12 right-handed women Let W = total number of women in the group So, 25% of W = 12 Rewrite as: 0.25W = 12 Solve: W = 12/0.25 = 48 So, there are 48 women So, the number of men in the ...”
February 10, 2019
GMATGuruNY posted a reply to Working together, Machine A and Machine B can produce a tota in the Data Sufficiency forum
“Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour. To determine A''s time to produce 200 widgets, we need to know A''s rate. Question stem, rephrased: What is A''s rate? Statement 1: Since B takes 5 hours to produce 50 widgets, ...”
February 10, 2019
Brent@GMATPrepNow posted a reply to Triangle XYZ is an isosceles right triangle. If side XY is l in the Problem Solving forum
“Triangle XYZ is an isosceles right triangle. Let''s sketch an isosceles right triangle: https://i.imgur.com/N3UOppf.png Side XY is longer than side YZ Since the hypotenuse is the longest side of a right triangle, side XY must be the hypotenuse. Add this to our diagram: ...”
February 9, 2019
GMATGuruNY posted a reply to Triangle XYZ is an isosceles right triangle. If side XY is l in the Problem Solving forum
“The sides of an isosceles right triangle are in the following ratio: x - x - x√2, where x and x constitute the base and height and x√2 is the hypotenuse. Since the triangle has a base of x, a height of x, and an area of 16, we get: (1/2)(x)(x) = 16 x² = 32 x = √32 Since XY is longer ...”
February 9, 2019
GMATGuruNY posted a reply to Machines X and Y work at their respective constant rates. Ho in the Data Sufficiency forum
“Statement 1: Time and rate are RECIPROCALS. Since X and Y together take 2/3 as long as X alone, X and Y together work 3/2 as fast as X alone. Thus, if X''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that Y''s rate alone = 3-2 = 1 unit ...”
February 9, 2019
GMATGuruNY posted a reply to Seven children — A, B, C, D, E, F, and G — are going to in the Problem Solving forum
“Since A and B must occupy adjacent positions, consider AB a single element in the arrangement. The number of ways to arrange the 6 elements AB, C, D, E, F and G = 6! = 720. In 1/2 of these arrangements, C will be to the LEFT of AB. In the remaining 1/2 of these arrangements,C will be to the ...”
February 9, 2019
fskilnik@GMATH posted a reply to Is abc at least 4? in the Data Sufficiency forum
“Hi, Mitch! Thanks for the words and for your beautiful contribution! $$abc\,\,\mathop \ge \limits^? \,\,4$$ $$\left( 1 \right)\,\,b + c\,\, \ge 2\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} ...” February 8, 2019 GMATGuruNY posted a reply to Is abc at least 4? in the Data Sufficiency forum “Nice problem, Fabio! Statement 1: Case 1: a=4, b=1 and c=1, with the result that b+c≥2 In this case, abc = 4, so the answer to the question stem is YES. Case 2: a=0, b=1 and c=1, with the result that b+c≥2 In this case, abc = 0, so the answer to the question stem is NO. Since the answer ...” February 8, 2019 GMATGuruNY posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum “Statement 1: If n=5, then the remainder when n is divided by 6 = 5/6 = 0 R5. If n=10, then the remainder when n is divided by 6 = 10/6 = 1 R4. Since different remainders are possible, INSUFFICIENT. Statement 2: Since n is a multiple of 12, n must also be a multiple of 6, with the result that ...” February 8, 2019 GMATGuruNY posted a reply to An electrical supplies store sells 140 power stabilizer in the Problem Solving forum “Since at least 5600 in profit must be earned by 140 units, the minimum required markup per unit = 5600/140 = 40. Thus, the minimum selling price = (cost per unit) + (minimum required markup per unit) = 16+40 = 56. The correct answer is D.” February 8, 2019 fskilnik@GMATH posted a new topic called Is abc at least 4? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14)$${\rm{Is}}\,\,abc\,\, \ge \,\,4\,\,\,?\left( 1 \right)\,\,b + c \ge 2\left( 2 \right)\,\,ab \ge ac \ge 4$$Answer: ____(C)__” February 8, 2019 Brent@GMATPrepNow posted a reply to Out of 2 broken TV sets and 6 fixed TV sets in Joe's Fix-My- in the Problem Solving forum “There are 8 TV''s in total 2 are broken 6 are fixed We want to find P(at least one TV is broken) When it comes to probability questions involving at least, it''s often best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting ...” February 8, 2019 Brent@GMATPrepNow posted a reply to An electrical supplies store sells 140 power stabilizer in the Problem Solving forum “Let x = the selling price per unit So, x - 16 = the PROFIT on ONE unit And 140(x - 16) = the PROFIT on the sale of 140 units (aka the weekly profit) What is the minimum selling price per unit that will ensure a weekly profit of at least 5600 from sales of power stabilizers? In other words, ...” February 8, 2019 Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum “Target question: What is the remainder when the positive integer n is divided by 6? Statement 1: n is multiple of 5 Let''s TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 10. In this case, the answer to the target question is the ...” February 8, 2019 fskilnik@GMATH posted a reply to If x, y, z are positive integers, is xyz ≥ 64? in the Data Sufficiency forum “Excellent problem, Max. Congrats!$$x,y,z\,\, \ge 1\,\,{\rm{ints}}xyz\,\,\mathop \ge \limits^? \,\,64\left( 1 \right)\,\,xy \ge yz \ge xz \ge 16\left\{ \matrix{ \,\left( {yz} \right)x \ge 16x \hfill \cr \,\left( {xz} \right)y \ge 16y \hfill \cr \,\left( {xy} ...”
February 8, 2019
fskilnik@GMATH posted a reply to In the last elections, three small political parties had 90, in the Problem Solving forum
“$$a,b,c\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,:\,\,\,{\rm{numbers}}\,\,{\rm{of}}\,\,{\rm{daily}}\,\,{\rm{TV}}\,\,{\rm{appearances}}$$ $$t\, \ge 1\,\,{\mathop{\rm int}} \,\,\,:\,\,{\rm{max}}\,\,\left( * \right)\,\,\,{\rm{number}}\,\,{\rm{of}}\,\,{\rm{seconds/appearance}}$$ $$? = a + b + c$$ $$\left. ...” February 8, 2019 fskilnik@GMATH posted a reply to Adriana´s room contains N identical light bulbs with indepe in the Problem Solving forum “$$?\,\,\,:\,\,\,N \ge 4\,\,{\mathop{\rm int}} \,\,{\rm{such}}\,\,{\rm{that}}\,\,\,B\left( N \right) = 26\,,\,\,\,{\rm{where}}\,\,\,B\left( N \right) = C\left( {N,2} \right) + C\left( {N,3} \right) + \ldots + C\left( {N,N} \right)\,\,\,\,\,\,\,\left( * \right)\left( {\rm{A}} \right)\,\,\,N ...”
February 8, 2019
fskilnik@GMATH posted a reply to The product of the positive 4-digit integer 118A and 25847 in the Problem Solving forum
“$$\left\langle {118A} \right\rangle \cdot 25847 + 4758 = 5M + 1\,\,\,,\,\,\,M \ge 1\,\,{\mathop{\rm int}}$$ $$?\,\,\,:\,\,\,\# \,\,A\,\,{\rm{possibilities}}$$ $$\leftThe correct answer is therefore (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” February 8, 2019 GMATGuruNY posted a reply to In the xy coordinate plane, line L and line K intersect at in the Data Sufficiency forum “Statement 1: The product of the x-intercepts of line L and K is positive. K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive: http://s4.postimage.org/ie5nbe78/lines_l_and_k_1.jpg K has a positive x-intercept, L has a positive x-intercept, the ...” February 8, 2019 GMATGuruNY posted a reply to If x and y are positive integers, is x an even integer? in the Data Sufficiency forum “Statements combined: Case 1: x=1 and y=1, with the result that x(y+5) = 6 and 6y²+41y+25 = 72 In this case, x is ODD, so the answer to the question stem is NO. Case 2: x=2 and y=1, with the result that x(y+5) = 12 and 6y²+41y+25 = 72 In this case, x is EVEN, so the answer to the question ...” February 7, 2019 GMATGuruNY posted a reply to What is the average (arithmetic mean) of x and y? in the Data Sufficiency forum “SUM = (COUNT)(AVERAGE). Statement 1: x+y+k = (count)(average) = 3*7 = 21. No way to determine the value of x+y. INSUFFICIENT. Statement 2: x+y+3k = (count)(average) = 3*13 = 39. No way to determine the value of x+y. INSUFFICIENT. Statements combined: Subtracting x+y+k=21 from ...” February 7, 2019 GMATGuruNY posted a reply to If a and b are integers, is a + b + 3 an odd integer? (1) in the Data Sufficiency forum “a+b+3 = ODD only if a and b are both odd or both even. Question stem, rephrased: Are a and b both odd or both even? Statement 1: ab = ODD implies that a and b are both odd. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: a-b = EVEN implies that a and b are either ...” February 7, 2019 Brent@GMATPrepNow posted a reply to What is the sum of the digits of the number (2^{2018})(5^{20 in the Problem Solving forum “Useful rule: (x^k)(y^k) = (xy)^k Example: (3^4)(7^4) = 21^4 (2^2018)(5^2019)(3^2) = (2^2018)((5^2018)(5^1))(3^2) = (2^2018)(5^2018)(5^1))(3^2) = (10^2018)(5^1))(3^2) = (10^2018)(5)(9) = (10^2018)(45) We know that (10^2018) = 1 followed by 2018 zeros So, (10^2018)(45) = 45 followed by ...” February 7, 2019 Brent@GMATPrepNow posted a reply to If a and b are integers, is a + b + 3 an odd integer? (1) in the Data Sufficiency forum “Target question: Is a + b + 3 an odd integer? Given: a and b are integers Statement 1: ab is an odd integer. Some useful rules: 1. ODD - ODD = EVEN 2. ODD - EVEN = ODD 3. EVEN - ODD = ODD 4. EVEN - EVEN = EVEN 5. (ODD)(ODD) = ODD 6. (ODD)(EVEN) = EVEN 7. (EVEN)(EVEN) = EVEN ...” February 7, 2019 Brent@GMATPrepNow posted a reply to The sides of a right triangle are consecutive even integers, in the Problem Solving forum “GIVEN: p = length of the longest side Since the side lengths are consecutive even integers, we can say: p - 2 = length of the 2nd longest side p - 4 = length of the shortest side NOTE: The longest side is the HYPOTENUSE. So, p = length of the HYPOTENUSE And p - 2 = length of one leg of ...” February 7, 2019 Brent@GMATPrepNow posted a reply to In the diagram above, O is the center of the circle. What is in the Data Sufficiency forum “Target question: What is the length of chord AC? Given: O is the center of the circle If O is the center of the circle, then AB is the circle''s DIAMETER If AB is the DIAMETER, then ∠C = 90°, because ∠C is an inscribed angle containing ("holding") the diameter. So, let''s ...” February 7, 2019 fskilnik@GMATH posted a new topic called The product of the positive 4-digit integer 118A and 25847 in the Problem Solving forum “GMATH practice exercise (Quant Class 16) The product of the positive 4-digit integer 118A and 25847 is 4758 units less than a number that leaves remainder 1 when divided by 5. How many values are possible for the digit A? (A) None (B) Only 1 (C) Only 2 (D) Only 3 (E) More than 3 ...” February 7, 2019 Brent@GMATPrepNow posted a reply to Ten telegenic contestants with a variety of personality diso in the Problem Solving forum “Let''s take the task of creating the teams and break it into stages. Stage 1: Select two 5 contestants to be in tribe A Since the order in which we select the contestants does not matter, we can use combinations. We can select 5 contestants from 10 contestants in 10C5 ways 10C5 = ...” February 7, 2019 fskilnik@GMATH posted a new topic called Adriana´s room contains N identical light bulbs with indepen in the Problem Solving forum “GMATH practice exercise (Quant Class 18) Adriana´s room contains N identical light bulb_s with independent switches, and this room is considered well lighted only if at least two of the light bulb_s are switched on. If there are exactly 26 different ways to make Adriana´s room well lighted, ...” February 7, 2019 fskilnik@GMATH posted a new topic called In the last elections, three small political parties had 90, in the Problem Solving forum “GMATH practice question (Quant Class 16) In the last elections, three small political parties had 90, 108 and 144 seconds for daily propaganda in television. If all three parties had different daily numbers of propaganda appearances, but all appearances took the same maximum possible number of ...” February 7, 2019 fskilnik@GMATH posted a reply to If the polynomial p in the variable x is defined by p(x) = in the Data Sufficiency forum “$$p\left( x \right) = k{x^2} - kx - 12\,\,\,\,\,\left( * \right)? = k\left( 1 \right)\,\,\,0\,\, = \,\,p\left( 3 \right)\,\,\mathop = \limits^{\left( * \right)} \,\,k{\left( 3 \right)^2} - k\left( 3 \right) - 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, ...”
February 7, 2019
fskilnik@GMATH posted a reply to The circle with center (1,0) and radius 5 intercepts at poin in the Problem Solving forum
“$$? = w + z = {x_M} + {y_M}\,\,\,\,\,\leftThe correct answer is therefore (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” February 7, 2019 fskilnik@GMATH posted a reply to What is the value of x ? in the Data Sufficiency forum “$$? = x\left( 1 \right)\,\,\,x > 0\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr} \right.\left( 2 \right)\,\,\,{\left( {{2^x}} \right)^3} - 12 \cdot {\left( {{2^x}} ...”
February 7, 2019
fskilnik@GMATH posted a reply to If x and y are integers, is x^2-y^2 odd? in the Data Sufficiency forum
“$$x,y\,\,{\rm{ints}}\,\,\,\,\,\left( * \right)$$ $${x^2} - {y^2}\,\,\mathop = \limits^? \,\,{\rm{odd}}$$ First Approach: ("the smart way") $$\left( 1 \right)\,\,x + y\,\,{\rm{odd}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} ...” February 7, 2019 fskilnik@GMATH posted a new topic called If x and y are integers, is x^2-y^2 odd? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 16) If x and y are integers, is x^2-y^2 odd? (1) x+y is odd (2) x-y is odd Answer: _____(D)___” February 6, 2019 fskilnik@GMATH posted a reply to We define the harmonic mean of a set of numbers as the recip in the Problem Solving forum “$$? = H\left( {20,30} \right)?\,\,\, = \,\,\,{1 \over {\mu \left( {{1 \over {20}} + {1 \over {30}}} \right)}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over {\,\,{1 \over {24}}\,\,}}\,\,\, = \,\,\,24\left( * \right)\,\,\,\,\,\mu \left( {{1 \over {20}} + {1 \over {30}}} \right) ...”
February 6, 2019
Brent@GMATPrepNow posted a reply to We define the harmonic mean of a set of numbers as the recip in the Problem Solving forum
“What is the harmonic mean of 20 and 30? NOTE: 20 = 20/1 So, the reciprocal of 20 = 1/20 And the reciprocal of 30 = 1/30 The average of 1/20 and 1/30 = (1/20 + 1/30 )/2 = (3/60 + 2/60 )/2 = (5/60 )/2 = (5/60 )/(2/1) = (5/60 )(1/2) = 5/120 The reciprocal of 5/120 = 120/5 = 24 Answer: ...”
February 6, 2019
fskilnik@GMATH posted a new topic called What is the value of x ? in the Data Sufficiency forum
“https://i.ibb.co/YcvpLGs/06-Feb19-5m.gif GMATH practice exercise (Quant Class 14) Answer: _____(B)__”
February 6, 2019
Brent@GMATPrepNow posted a reply to A certain bag contains red, blue, and green marbles. What is in the Data Sufficiency forum
“ Given: A certain bag contains red, blue, and green marbles. Let R = # number red marbles in the bag Let B = # number blue marbles in the bag Let G = # number green marbles in the bag Target question: What is the value of G/R? Statement 1: The number of blue marbles in the bag is two ...”
February 6, 2019
fskilnik@GMATH posted a new topic called The circle with center (1,0) and radius 5 intercepts at poin in the Problem Solving forum
“GMATH practice exercise (Quant Class 20) The circle with center (1,0) and radius 5 intercepts at points A and B the straight line defined by C = (0,0) and D= (4,8). If M = (w,z) is the midpoint of the line segment AB, what is the value of w+z ? (A) 3/7 (B) 1/2 (C) 3/5 (D) 3/4 (E) 1 ...”
February 6, 2019
Brent@GMATPrepNow posted a reply to If x is a nonzero number, which of the three numbers x, 1/x in the Data Sufficiency forum
“ Given: x is a nonzero number Target question: Which of the three numbers x, 1/x and x² is greatest? Statement 1: -1 < x < 1 This statement doesn''t FEEL sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = ...”
February 6, 2019
fskilnik@GMATH posted a new topic called If p(x) = kx^2-kx-12 for all values of x, what is the value in the Data Sufficiency forum
“https://i.ibb.co/S71XmCJ/07-Feb19-2b.gif GMATH practice exercise (Quant Class 14) Answer: ______(D)___”
February 6, 2019
fskilnik@GMATH posted a reply to The water tank shown is a prism, consisting of 3 rectangular in the Problem Solving forum
“https://i.ibb.co/ysCFC1L/05-Feb19-6v.gif $$?\,\, \cong \,\,x$$ $$\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} ...” February 6, 2019 fskilnik@GMATH posted a reply to Which of the following may be correctly expressed by the gra in the Problem Solving forum “ FOCUS: graph association From the figure given: > We expect y to decrease whenever |x| increases, in other words, whenever x > 0 gets larger or x < 0 gets smaller (i.e., more negative). > This is enough to refute (A) and (B). > We expect y to be defined for all values of ...” February 6, 2019 fskilnik@GMATH posted a reply to If a > b > c > d > 0, is d < 4? in the Data Sufficiency forum “$$a > b > c > d > 0\,\,\,\,\, \Rightarrow \,\,\,\,0 < {1 \over a} < {1 \over b} < {1 \over c} < {1 \over d}\,\,\,\,\left( * \right)d\,\,\mathop < \limits^? \,\,4\left( 1 \right)\,\,{1 \over c} + {1 \over d} > {1 \over 2}\,\,\,\,\mathop \Rightarrow ...”
February 5, 2019
fskilnik@GMATH posted a new topic called Which of the following functions may be expressed by the gra in the Problem Solving forum
“https://i.ibb.co/hWG6HXC/05-Fev19-8j.gif GMATH practice exercise (Quant Class 4) Which of the following may be correctly expressed by the graph representation given above? (A) y = |x|^2 (B) y = 2^x (C) y = x^(-1/2) (D) y = x^(-1) (E) y = x^(-2) Answer: _____(E)__”
February 5, 2019
GMATGuruNY posted a reply to In the coordinate plane, Line A has a slope of -1 and an in the Problem Solving forum
“Line A includes points (1, 0) and (a, b) and has a slope of -1. Thus: (b - 0)/(a-1) = -1 b = -a + 1 a+b = 1. The correct answer is B. The information about Line B is irrelevant.”
February 5, 2019
GMATGuruNY posted a reply to In how many ways can a 4-letter word be formed from the in the Problem Solving forum
“Alternate approach: Case 1: VVCC, where the first two letters are vowels and the last 2 letters are consonants Number of options for the first vowel = 4. (Any of the 4 vowels) Number of options for the second vowel = 3. (Any of the 3 remaining vowels) Number of options for the first consonant ...”
February 5, 2019
fskilnik@GMATH posted a new topic called The water tank shown is a prism, consisting of 3 rectangular in the Problem Solving forum
“https://i.ibb.co/pwhKHZ9/05-Feb19-5z.gif GMATH practice exercise (Quant Class 17) The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the ...”
February 5, 2019
Brent@GMATPrepNow posted a reply to Three sisters have an average (arithmetic mean) age of 25 in the Problem Solving forum
“If the average age is 25, we can write: (sum of all 3 ages)/3 = 25 This means, the sum of all 3 ages = 75 If the median is 24, then we can express the ages in ascending order as follows: __ , 24, __ Since the sum of the ages is 75, we can MINIMIZE the age of the oldest girl by MAXIMIZING the ...”
February 5, 2019
fskilnik@GMATH posted a reply to If (x-7)^2=-|y-5|, xy=? in the Problem Solving forum
“$${\left( {x - 7} \right)^2} = - \left| {y - 5} \right|\,\,\,\,\,\left( * \right)$$ $$? = xy$$ $$\left. \matrix{ {\left( {x - 7} \right)^2} \ge 0\,\,\, \hfill \cr - \left| {y - 5} \right| \le 0 \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} ...” February 5, 2019 fskilnik@GMATH posted a reply to If a and b are constants such that ... in the Problem Solving forum “https://i.ibb.co/1X87H4N/05-Feb19-2k.gif” February 5, 2019 fskilnik@GMATH posted a reply to The image shows an office key holder where 8 different keys in the Problem Solving forum “ ? = # of 8-keys placing ? = P2 (main keys) * P6 (other keys) = 2! * 6! = 2 * 720 = 1440. The correct answer is therefore (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” February 5, 2019 fskilnik@GMATH posted a reply to In the figure shown, the square ABCD is inscribed in the tri in the Data Sufficiency forum “https://i.ibb.co/d7bR1D0/04-Feb19-11d.gif$$? = 4x\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = x\,}$$Each statement alone is not sufficient, as proved by the geometric bifurcations presented in the figure above.$$\left( {1 + 2} \right)\,\,\,\Delta EAB\,\, \cong \,\,\Delta ...”
February 5, 2019
Brent@GMATPrepNow posted a reply to A contractor combined x tons of a gravel mixture that in the Data Sufficiency forum
“Let''s use some weighted averages to solve this question Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Target question: What is the value of x ? Given: A contractor combined x ...”
February 4, 2019
GMATGuruNY posted a reply to A contractor combined x tons of a gravel mixture that in the Data Sufficiency forum
“x = 10% gravel y = 2% gravel. z = the MIXTURE of x and y = 5% gravel. To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the ...”
February 4, 2019
fskilnik@GMATH posted a new topic called The image shows an office key holder where 8 different keys in the Problem Solving forum
“https://i.ibb.co/mbYL9rR/04-Feb19-12u.gif <b>GMATH</b> practice question (Quant Class 18) The image shows an office key holder where 8 different keys must be placed (one key per square). If the two main keys must be placed in the blue squares, in how many ways can all the keys be ...”
February 4, 2019
fskilnik@GMATH posted a new topic called In the figure shown, the square ABCD is inscribed in the tri in the Data Sufficiency forum
“https://i.ibb.co/s2Svrff/04-Feb19-9h.gif <b>GMATH</b> &nbsp;practice question &nbsp;(Quant Class 17) In the figure shown, the square ABCD is inscribed in the triangle EFG. What is the perimeter of the square? (1) FG = 10 (2) The distance from E to the line FG is 6. ...”
February 4, 2019
fskilnik@GMATH posted a new topic called If a and b are constants such that ... in the Problem Solving forum
February 4, 2019
Brent@GMATPrepNow posted a reply to A committee of 6 is chosen from 8 men and 5 women so as to in the Problem Solving forum
“Since the committee must have 6 people, there are two cases that meet the given restrictions: 1) The committee has 2 men and 4 women 2) The committee has 3 men and 3 women 1) The committee has 2 men and 4 women Since the order in which we select the men and women does not matter, we can use ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to Mixture problem unclear in the Problem Solving forum
“When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED. Since we''re asked to find a PERCENTAGE, we can assign a "nice" value to the original volume. So, let''s say we start with 100 liters https://i.imgur.com/yt2KAw7.png As you can ...”
February 4, 2019
Brent@GMATPrepNow posted a reply to Mr. Jones spends $25 on movie tickets for a party of adults in the Data Sufficiency forum “ Given: Mr. Jones spends$25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost $3 each and children''s tickets cost$2 each. There are several scenarios that satisfy statement 1. Here are ...”
February 4, 2019
fskilnik@GMATH posted a reply to In a certain sock drawer, there are 4 pairs of black socks, in the Problem Solving forum
“Excellent approach! In our method we call it the "Murphy´s Law argument": if something can (still) go wrong, it will! (Brent´s wording is perfect: three socks may go wrong, but the fourth´s cannot. That´s why the answer is 4, indeed.) Regards, Fabio.”
February 4, 2019
Brent@GMATPrepNow posted a reply to In a certain sock drawer, there are 4 pairs of black socks, in the Problem Solving forum
“If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don''t have a matching sock. So, we can select 3 socks WITHOUT having a matching pair. However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected. Answer: A Cheers, Brent”
February 4, 2019
fskilnik@GMATH posted a reply to Mr. Jones spends \$25 on movie tickets for a party of adults in the Data Sufficiency forum
“$$\left\{ \matrix{ \,A\,\,{\rm{adults}}\,\,{\rm{,}}\,\,\,{{\rm{p}}_{\rm{A}}} = {\rm{cost}}\,\,\left( {\rm{\ }} \right)\,\,{\rm{per}}\,\,{\rm{ticket}} \hfill \cr \,C\,\,{\rm{children}}\,\,{\rm{,}}\,\,\,{{\rm{p}}_{\rm{C}}} = {\rm{cost}}\,\,\left( {\rm{\ }} ...” February 4, 2019 fskilnik@GMATH posted a reply to If x, y are integers, is (x-y)(x+y)(x^2+y^2) an odd number? in the Data Sufficiency forum “$$x,y\,\,{\rm{ints}}\,\,\,\left( * \right)A\left( {x,y} \right) = \left( {x - y} \right)\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)\,\,\,\mathop = \limits^? \,\,\,{\rm{odd}}\left( 1 \right)\,\,x\,\,{\rm{odd}}\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = ...”
February 4, 2019