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In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % of women are homeowners.

In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % of women are homeowners. What is the least number of members who are homeowners?

A. 49
B. 47
C. 45
D. 43
E. 41

Answer: E

Source: Official Guide


In a sequence of terms in which each term is three times the previous term, what is the fourth term?

In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is \(3.\)

(2) The second-to-last term is \(3^{10.}\)

Answer: A

Source: Manhattan GMAT


For a party, three solid cheese balls with diameters of \(2\) inches, \(4\) inches, and \(6\) inches, respectively, were

For a party, three solid cheese balls with diameters of \(2\) inches, \(4\) inches, and \(6\) inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is \(\dfrac43\pi r^3,\) where \(r\) is the rad...


Set \(X\) consists of exactly four distinct integers that are greater than \(1.\) For each integer in the set, all of

Set \(X\) consists of exactly four distinct integers that are greater than \(1.\) For each integer in the set, all of that integer’s unique prime factors are also in the set. For example, if \(20\) is in set \(X,\) then \(2\) and \(5\) must also be in set \(X.\) How many of the distinct integers in ...


A set of 12 test scores has an average of 500 and a standard deviation of 50. Which of the following sets of additional

A set of 12 test scores has an average of 500 and a standard deviation of 50. Which of the following sets of additional test scores, when combined with the original set of 12 test scores, must result in a combined data set with a standard deviation less than 50? (A) 6 test scores with an average of ...


Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the

Two pieces of fruit are selected out of a group of 8 pieces of fruit consisting only of apples and bananas. What is the probability of selecting exactly 2 bananas? (1) The probability of selecting exactly 2 apples is greater than 1/2. (2) The probability of selecting 1 apple and 1 banana in either o...


For all positive integers \(n,\) the sequence \(A_n\) is defined by the following relationship:

For all positive integers \(n,\) the sequence \(A_n\) is defined by the following relationship: \(A_n=\dfrac{n-1}{n!}.\) What is the sum of all the terms in the sequence from \(A_1\) through \(A_{10},\) inclusive? (A) \(\dfrac{9!+1}{10!}\) (B) \(\dfrac{9(9!)}{10!}\) (C) \(\dfrac{10!-1}{10!}\) (D) \(...


If \(a\) and \(b\) are nonzero numbers on the number line, is \(0\) between \(a\) and \(b?\)

If \(a\) and \(b\) are nonzero numbers on the number line, is \(0\) between \(a\) and \(b?\) (1) The distance between \(0\) and \(a\) is greater than the distance between \(0\) and \(b.\) (2) The sum of the distances between \(0\) and \(a\) and between \(0\) and \(b\) is greater than the distance be...


A pharmaceutical company received \(\$3\) million in royalties on the first \(\$20\) million in sales of the generic

A pharmaceutical company received \(\$3\) million in royalties on the first \(\$20\) million in sales of the generic equivalent of one of its products and then \(\$9\) million in royalties on the next \(\$108\) million in sales. By approximately what percent did the ratio of royalties to sales decre...


If \(|12x - 3| = |3x + 15|,\) what is the value of \(x?\)

If \(|12x - 3| = |3x + 15|,\) what is the value of \(x?\)

(1) \(x > 0\)
(2) \(x\) is an integer.

Answer: D

Source: Veritas Prep

by Vincen

Fri Jan 28, 2022 4:47 am
Forum: Data Sufficiency
Topic: If \(|12x - 3| = |3x + 15|,\) what is the value of \(x?\)
Replies: 0
Views: 8

A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points

farmland.png A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is \(4\) kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as l...


Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped

Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped out of the tank at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the tank increasing? (1) The amount of water initially in...


If \((x + y)^2 = 16\) and \(x^2 - y^2 = 16,\) what is the value of \(2x^2?\)

If \((x + y)^2 = 16\) and \(x^2 - y^2 = 16,\) what is the value of \(2x^2?\)

(A) 8
(B) 16
(C) 18
(D) 32
(E) 50

Answer: D

Source: Manhattan GMAT


In the sequence of positive numbers \(x_1, x_2, x_3, \ldots,\) what is the value of \(x_1?\)

In the sequence of positive numbers \(x_1, x_2, x_3, \ldots,\) what is the value of \(x_1?\)

(1) \(x_i=\dfrac{x_{i-1}}2\) for all integers \(i>1.\)

(2) \(x_5=\dfrac{x_4}{x_4+1}\)

Answer: C

Source: GMAT Prep


A multiple-choice test consists of 4 questions, and each question has 5 answer choices. In how many ways can the test be

A multiple-choice test consists of 4 questions, and each question has 5 answer choices. In how many ways can the test be completed if every question is unanswered?

A) 24
B) 120
C) 625
D) 720
E) 1024

Answer: C

Source: Veritas Prep