If x > y > z, which of the following could be… | GMAT Sprint

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PS · Problem Solving

705-805

Divisibility/Multiples/Factors

If $x > y > z$ , which of the following could be true?
I. $x^3 > y^3 > z^3$
II. $z > y^2 > x^3$
III. $x^3 > z^3 > y^3$

Answer Choices

Correct answer marked below

I only

II only

I and II only

Correct

I and III only

I, II, and III

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Explanation

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Official Explanation

Official

x^3 > y^3 > z^3

: We can ALWAYS raise an inequality to a positive odd power (the same for taking a positive odd root from an inequality). So, if

x > y > z

, then

x^3 > y^3 > z^3

x^5 > y^5 > z^5

x^7 > y^7 > z^7

, will always be true.

II.

z > y^2 > x^3

: In this option we have reversed order when raised to positive powers, so we immediately should think of positive proper fractions (fractions from 0 to 1). For example, if

x > y > z

0.3 > 0.2 > 0.1

, then

z > y^2 > x^3

would be

0.1 > 0.2^2 > 0.3^3

, which is correct.…

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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.

If x>y>zx > y > zx>y>z, which of the following could be true?I. x3>y3>z3x^3 > y^3 > z^3x3>y3>z3II. z>y2>x3z > y^2 > x^3z>y2>x3III. x3>z3>y3x^3 > z^3 > y^3x3>z3>y3