Consider positive integers x, y, and z, all g… | GMAT Sprint

Free Practice Question

PS · Problem Solving

605-655

Divisibility/Multiples/Factors

Consider positive integers x, y, and z, all greater than 1. If x and y are divisors of z, which of the following must also be a divisor of $z^{(xy)}$ ?

I. $x+y$
II. $y^x$
III. $x^2 * y^2$

Answer Choices

Correct answer marked below

I only

II only

III only

I and II

II and III

Correct

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Explanation

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Official Explanation

Official

Given that x, y, and z are positive integers greater than 1, and both x and y are divisors of z, we need to determine which of the following must be a divisor of

z^{(xy)}

. First, since x and y are factors of z, we can express z as

z = kxy

for some integer k. Therefore,

z^{(xy)} = (kxy)^{(xy)} = k^{(xy)} * x^{(xy)} * y^{(xy)}

. This shows that both…

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Comments

TrangApr 9, 2025

greatt question!

khanJul 9, 2024

Thank you very much!

ThomasAug 3, 2024

Thank for sharing!

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

Consider positive integers x, y, and z, all greater than 1. If x and y are divisors of z, which of the following must also be a divisor of z(xy)z^{(xy)}z(xy)? I. x+yx+yx+y II. yxy^xyx III. x2∗y2x^2 * y^2x2∗y2