Given that |xy| > xy, which of the following… | GMAT Sprint

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PS · Problem Solving

sub-505

Absolute Values/Modules

Given that $|xy| > xy$ , which of the following statements must hold true?

I. $x < 0$

II. $y < 0$

III. $xy < 0$

Answer Choices

Correct answer marked below

I only

II only

III only

Correct

I and III

II and III

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Explanation

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Official Explanation

Official

Since

|xy| > xy

, it implies that

xy < 0

. Now, let's analyze the statements:

I.

x < 0

is not necessarily true because x could be positive while y is negative.

II.

y < 0

is also not necessarily true as y could be positive while x is negative.…

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Comments

ParveenSep 3, 2024

thanks a lot

HəmidzadəJan 30, 2025

Thanks

What this question tests

What it tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Common trap

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.

Given that ∣xy∣>xy|xy| > xy∣xy∣>xy, which of the following statements must hold true? I. x<0x < 0x<0 II. y<0y < 0y<0 III. xy<0xy < 0xy<0