Given that x < 0 and 0 < y < |x|, which of th… | GMAT Sprint

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PS · Problem Solving

sub-505

Absolute Values/Modules

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

Correct answer marked below

y^2 − x^2 < 0

Correct

x^2 − y^2 < 0

(y − x)^2 < 0

(x − y)^2 < 0

(x + y)^2 < 0

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Explanation

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Official Explanation

Official

Given: If

x < 0

and

0 < y < |x|

.

To find: which of the following must be true?

Solution:

Y is less than |x| and X is negative.

Let Y = 2 and X = -3.

A.

y^2−x^2<0: 2^2 - (-3)^2 < 0, 4 - 9 < 0, -5 < 0

(TRUE).

B.

x^2−y^2<0: (-3)^2 - 2^2 < 0, 9 - 4 < 0, 5 < 0

(WRONG).…

Comments

varshinJul 12, 2024

thanks!

gokulMay 10, 2024

thank you for sharing

What this question tests

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

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