If x is a positive integer, is x x an integer? (1) 4x is an integer. (2) 3x is not an integer.

Free Practice Question

DS · Data Sufficiency

505-555

Algebra

If $x$ is a positive integer, is $x \sqrt{x}$ an integer?

(1) $\sqrt{4x}$ is an integer.
(2) $\sqrt{3x}$ is not an integer.

Correct answer marked below

Statement (1) ALONE is sufficient

Correct

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient

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Explanation

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Comments

Chynna6d ago

Thanks, this one was nice and quick. Statement 1 basically forces x to be a perfect square times something, so it works out.

Shreyajust now

wait, does it really force a perfect square? I just tested x=4 and x=9 and it held

RaparthyMay 26

hmm I got stuck deciding between A and D because I thought statement 2 was doing something too. then realized it's only telling us what ISN'T true

VishnuSep 14

Is x√x the same as x^(3/2)? If so then x needs to be a perfect square for that exponent to come out whole... that's how I reasoned it anyway

What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.