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:

Brilliant question!! My initial thought was sqrt2 is a valid remainder. Haha. Surprising how assumptions can kill you!! Although I chose B (a good guess!)

I plugged in x is sqrt2, then argued with myself that Y can be four and the statement will hold true.

So, takeaway from this is REMAINDERS HAVE TO BE INTEGERS!

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) \(\frac{X}{Y}\) is not an integer.

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 \(y=4\);

I kinda agree with the above post by rongali. Here are my 2 cents:-

"Y cannot be an integer" is easily proved wrong since y can be zero and therefore XY will be divisible by 4.

If Y cannot be a positive integer, then, considering that GMAT revolves around only real numbers, Y can be Zero, a negative Integer, a positive fraction or a negative fraction. If Y is zero, then XY is always divisible by 4. If Y is a negative integer, then XY will not be divisible by 4. If Y is a positive fraction, then XY could be or could not be divisible by 4, and likewise if Y is a negative Fraction, then XY could be or could not be divisible by 4.

But i think the catch of the question is that we cannot prove the parent statement wrong. So considering that XY IS DIVISIBLE by 4, we will have to ignore the possibilities mentioned above that do no lead to a proper divisibility by 4. Therefore, we are left with Y=0 OR Y=Negative Fraction, that produces XY divisible by 4 OR Y=Positive Fraction that produces proper divisibility. All in All, we realize that Y cannot be a positive integer because in that case XY will never be divisible by 4. Phewww, i'm exhausted.

I kinda agree with the above post by rongali. Here are my 2 cents:-

"Y cannot be an integer" is easily proved wrong since y can be zero and therefore XY will be divisible by 4.

If Y cannot be a positive integer, then, considering that GMAT revolves around only real numbers, Y can be Zero, a negative Integer, a positive fraction or a negative fraction. If Y is zero, then XY is always divisible by 4. If Y is a negative integer, then XY will not be divisible by 4. If Y is a positive fraction, then XY could be or could not be divisible by 4, and likewise if Y is a negative Fraction, then XY could be or could not be divisible by 4.

But i think the catch of the question is that we cannot prove the parent statement wrong. So considering that XY IS DIVISIBLE by 4, we will have to ignore the possibilities mentioned above that do no lead to a proper divisibility by 4. Therefore, we are left with Y=0 OR Y=Negative Fraction, that produces XY divisible by 4 OR Y=Positive Fraction that produces proper divisibility. All in All, we realize that Y cannot be a positive integer because in that case XY will never be divisible by 4. Phewww, i'm exhausted.

nice question Answer is B. the thing is, Y is not positive integer. because if X=\sqrt{2}, Y must be either zero or non integer. it can be 4\sqrt{2} which is not positive integer. for short, assume B states if X=\sqrt{2}, Y is not integer (except 0)