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\(x,y\) are positive integers. Find the number of even factors of \(4x^2.\)

\(x,y\) are positive integers. Find the number of even factors of \(4x^2.\)

I. \(x^3-y^3+3xy\) is odd and \(x\) is a prime.
II. \(x^{x+y}\cdot y^{3x}+x^{3y}\) is odd.

Answer: C

Source: e-GMAT


\(\&, \#,\) and \(@\) each represents a different digit, and \(\&\) multiplied by \(\#\) is smaller than \(10.\) What is

\(\&, \#,\) and \(@\) each represents a different digit, and \(\&\) multiplied by \(\#\) is smaller than \(10.\) What is the value of the two-digit number \(\&\#\) if the following multiplication problem is true: \(\&\#\cdot \#\& = \#@\#\) (A) 11 (B) 12 (C) 13 (D) 21 (E) 31 Answer: B Source: Veritas...


If \(x\) and \(y\) are non-zero integers and \(|x| + |y| = 32,\) what is \(xy?\)

If \(x\) and \(y\) are non-zero integers and \(|x| + |y| = 32,\) what is \(xy?\)

(1) \(-4x - 12y = 0\)

(2) \(|x| - |y| = 16\)

Answer: A

Source: Manhattan GMAT


If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)

If \(x^{a+3}=y^{b+2},\) where \(x\) and \(y\) are distinct prime numbers, what is the value of \(ab?\)

A. -6
B. 0
C. 5
D. 6
E. It cannot be determined from the information provided.

Answer: D

Source: Princeton Review


Is the number \(x\) positive?

Is the number \(x\) positive?

(1) On the number line, \(0\) is closer to \(x - 1\) than to \(x.\)
(2) On the number line, \(0\) is closer to \(x\) than to \(x + 1.\)

Answer: A

Source: Manhattan GMAT

by Vincen

Fri Feb 11, 2022 3:17 am
Forum: Data Sufficiency
Topic: Is the number \(x\) positive?
Replies: 1
Views: 211

At a family summer party, each of the \(x\) members of the family chose whether or not to have a hamburger and whether

At a family summer party, each of the \(x\) members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If \(\dfrac13\) chose to have a hamburger, and of those \(\dfrac17\) chose to also have a hotdog, then how many family members chose NOT to have both? A. \(...


Is \(|x + 1| + |x - 2| < 4 ?\)

Is \(|x + 1| + |x - 2| < 4 ?\)

(1) \(x\) is between \(-0.5\) and \(4.\)
(2) \(x\) is between \(-2\) and \(2.5.\)

Answer: C

Source: Manhattan GMAT

by Vincen

Fri Feb 11, 2022 3:13 am
Forum: Data Sufficiency
Topic: Is \(|x + 1| + |x - 2| < 4 ?\)
Replies: 0
Views: 171

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...