## Search found 2898 matches

#### $$x,y$$ are positive integers. Find the number of even factors of $$4x^2.$$

##### $$x,y$$ are positive integers. Find the number of even factors of $$4x^2.$$

$$x,y$$ 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.

Source: e-GMAT

by Vincen

Wed Feb 23, 2022 3:51 am
Forum: Data Sufficiency
Topic: $$x,y$$ are positive integers. Find the number of even factors of $$4x^2.$$
Replies: 0
Views: 199

#### $$\&, \#,$$ 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

$$\&, \#,$$ 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 Answe...

#### 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 $$xy?$$

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

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

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

Source: Manhattan GMAT

by Vincen

Fri Feb 11, 2022 3:20 am
Forum: Data Sufficiency
Topic: If $$x$$ and $$y$$ are non-zero integers and $$|x| + |y| = 32,$$ what is $$xy?$$
Replies: 0
Views: 177

#### 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 $$ab?$$

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.

Source: Princeton Review

#### Is the number $$x$$ positive?

##### 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 $$x + 1.$$

Source: Manhattan GMAT

by Vincen

Fri Feb 11, 2022 3:17 am
Forum: Data Sufficiency
Topic: Is the number $$x$$ positive?
Replies: 1
Views: 226

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 $$|x + 1| + |x - 2| < 4 ?$$

Is $$|x + 1| + |x - 2| < 4 ?$$

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

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: 181

#### 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.

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

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?

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 $$3^{10.}$$

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

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

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

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

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: $$A_n=\dfrac{n-1}{n!}.$$ 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 $$b?$$

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...