Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If XY is divisible by 4, which of the following must be true [#permalink]

Show Tags

29 Nov 2008, 14:27

1

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

45% (01:14) correct 55% (01:09) wrong based on 382 sessions

HideShow timer Statistics

If XY is divisible by 4, which of the following must be true?

A. If X is even then Y is odd B. If X = sqrt(2) then Y is not a positive integer C. If X is 0 then X + Y is not 0 D. X^Y is even E. X/Y is not an integer

If XY is divisible by 4, which of the following must be true?

1. If X is even then Y is odd 2. If X = sqrt(2) then Y is not a positive integer 3. If X is 0 then X + Y is not 0 4. X^Y is even 5. X/Y is not an integer

Do we assume that both X and Y can be the same number? Does this go the same in the actual GMAT Test?

None. Seems the question is flawed.

1: It is not true if x = 2 and y = 2. 2: It is not true if y = 2 sqrt(2). Y doesnot need to be -ve. 3: It is not true if y = 0. 4: It is not true if x = 4 and y = 3. 5: It is not true if x = 4 and y = 2.

Only choice B must be true. If X is sqrt(2) then Y cannot be an integer, otherwise it would mean that XY is not an integer. Counter-examples to other answer choices:

If \(XY\) is divisible by 4, which of the following must be true?

* If \(X\) is even then \(Y\) is odd. * If \(X = \sqrt{2}\) then \(Y\) is not a positive integer. * If \(X\) is 0 then \(X + Y\) is not 0. * \(X^Y\) is even. * \(\frac{X}{Y}\) is not an integer.

Can someone explain how the answer is B? I feel even if x = rt2, Y can be a positive integer.

If \(XY\) is divisible by 4, which of the following must be true?

* If \(X\) is even then \(Y\) is odd. * If \(X = \sqrt{2}\) then \(Y\) is not a positive integer. * If \(X\) is 0 then \(X + Y\) is not 0. * \(X^Y\) is even. * \(\frac{X}{Y}\) is not an integer.

Can someone explain how the answer is B? I feel even if x = rt2, Y can be a positive integer.

\(X = \sqrt{2}\) and Y = 4

XY = (rt2 * 4) /4 which is divisible by 4 = rt2

The confusing part is the word "positive": If \(x=\sqrt{2}\), \(y\) can be positive as well as negative BUT it can not be an integer! It can not be positive integer.

\(y\) must be of a type of \(y=\sqrt{2}*2n\) where \(n\) is an integer, not necessarily positive. So \(y\) can be \(\sqrt{2}*8\), when \(n=4\) OR \(-\sqrt{2}*2\), when \(n=-1\) OR \(0\), when \(n=0\).

As when \(y=\sqrt{2}*2n\) and \(x=\sqrt{2}\), \(xy=4n\) and the condition that it's divisible by \(4\) holds true for any value of \(n\).
_________________

Bunuel - I still didn't get it why Y " must be". Why can Y not be positive or why can Y not be an integer??

The question states whether XY is divisible by 4. It does not state that the result of XY must be an integer. So even if X is \(\sqrt{2}\) , Y can be a multiple of 4 and XY can be divisible by 4, resulting in \(\sqrt{2}\)

Bunuel - I still didn't get it why Y " must be". Why can Y not be positive or why can Y not be an integer??

The question states whether XY is divisible by 4. It does not state that the result of XY must be an integer. So even if X is \(\sqrt{2}\) , Y can be a multiple of 4 and XY can be divisible by 4, resulting in \(\sqrt{2}\)

In the following:

X = \(\sqrt{2}\) and Y = 4

XY = 4\(\sqrt{2}\)

XY/4 = \(\sqrt{2}\) 4/4

=\(\sqrt{2}\)

First of all XY is divisible by 4 means that the product of XY is evenly divided by 4, the result must be an integer. So \(x=\sqrt{2}\) and \(y=4\), will not work as the result \(\sqrt{2}\) is not an integer.

Second Y can be positive. Y can not be positive integer. Y must have \(\sqrt{2}\) in it to "compensate" \(\sqrt{2}\) of \(X\), to turn their product, \(XY\), into the integer, so that \(XY\) to have a chance of divisibility by \(4\). When \(Y\) has \(\sqrt{2}\) in it, multiplied by \(X=\sqrt{2}\), the product will be an integer.

So: Y can be negative irrational number: \(-\sqrt{2}*2\), \(-\sqrt{2}*4\), \(-\sqrt{2}*6\), \(-\sqrt{2}*8\), etc; OR Y can be positive irrational number: \(\sqrt{2}*2\), \(\sqrt{2}*4\), \(\sqrt{2}*6\), \(\sqrt{2}*8\), etc; OR Y can be zero, then XY=0 and 0 is divisible by any number, including 4.

Re: If XY is divisible by 4, which of the following must be true [#permalink]

Show Tags

10 Nov 2012, 15:39

i think the thing that needs to be made clear is that whenever gmat says that a number is divisible by an integer then that implies that both the numerator and the denominator are integers and in our case XY product has to be integer.

i think the thing that needs to be made clear is that whenever gmat says that a number is divisible by an integer then that implies that both the numerator and the denominator are integers and in our case XY product has to be integer.

On GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that: 1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\).

So the terms "divisible", "multiple", "factor" ("divisor") are used only about integers (at least on GMAT).

BELOW IS REVISED VERSION OF THIS QUESTION:

If \(x\) and \(y\) are positive integer and \(xy\) is divisible by 4, which of the following must be true?

A. If \(x\) is even then \(y\) is odd. B. If \(x\) is odd then \(y\) is a multiple of 4. C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer. D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer. E. \(x^y\) is even.

Notice that the question asks which of the following MUST be true not COULD be true.

A. If \(x\) is even then \(y\) is odd --> not necessarily true, consider: \(x=y=2=even\);

B. If \(x\) is odd then \(y\) is a multiple of 4 --> always true: if \(x=odd\) then in order \(xy\) to be a multiple of 4 y mst be a multiple of 4;

C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer --> not necessarily true, consider: \(x=1\) and \(y=4\);

D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer --> not necessarily true, consider: \(x=2\) and \(y=4\);

E. \(x^y\) is even --> not necessarily true, consider: \(x=1\) and \(y=4\);

If XY is divisible by 4, which of the following must be true [#permalink]

Show Tags

03 Jan 2017, 12:06

Bunuel wrote:

study wrote:

If \(XY\) is divisible by 4, which of the following must be true?

* If \(X\) is even then \(Y\) is odd. * If \(X = \sqrt{2}\) then \(Y\) is not a positive integer. * If \(X\) is 0 then \(X + Y\) is not 0. * \(X^Y\) is even. * \(\frac{X}{Y}\) is not an integer.

Can someone explain how the answer is B? I feel even if x = rt2, Y can be a positive integer.

\(X = \sqrt{2}\) and Y = 4

XY = (rt2 * 4) /4 which is divisible by 4 = rt2

The confusing part is the word "positive": If \(x=\sqrt{2}\), \(y\) can be positive as well as negative BUT it can not be an integer! It can not be positive integer.

\(y\) must be of a type of \(y=\sqrt{2}*2n\) where \(n\) is an integer, not necessarily positive. So \(y\) can be \(\sqrt{2}*8\), when \(n=4\) OR \(-\sqrt{2}*2\), when \(n=-1\) OR \(0\), when \(n=0\).

As when \(y=\sqrt{2}*2n\) and \(x=\sqrt{2}\), \(xy=4n\) and the condition that it's divisible by \(4\) holds true for any value of \(n\).

Hi Bunuel Y can be zero too,which is an integer. Although it wont have any impact on the answer as 0 isn't positive. But y "can be an integer"