Given that y ≠ 0 and y^2 < |y|, which of the… | GMAT Sprint

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PS · Problem Solving

sub-505

Absolute Values/Modules

Given that $y ≠ 0$ and $y^2 < |y|$ , which of the following statements must hold true?

Answer Choices

Correct answer marked below

y > 2

y < -2

-1 < y < 1 and

y ≠ 0

Correct

|y| > 2

y = -2

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Explanation

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Official Explanation

Official

Since

y ≠ 0

and

y^2 < |y|

, we can manipulate the inequality.

Dividing both sides of the inequality

y^2 < |y|

by |y| (which is valid since |y| is always positive), we obtain

|y| < 1

.…

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Comments

AmishaSep 27, 2024

thanks a lot

RhythmJan 14, 2025

pls explain more?

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 y≠0y ≠ 0y=0 and y2<∣y∣y^2 < |y|y2<∣y∣, which of the following statements must hold true?