Which of the following expressions equals 0 w… | GMAT Sprint

Free Practice Question

PS · Problem Solving

555-605

Absolute Values/Modules

Which of the following expressions equals 0 when $x < 0$ and equals $x^2$ when $x ≥ 0$ ?

Correct answer marked below

x|x|

x + |x|

2x^2 - x|x|

\frac{1}{4}(x + |x|)^2

Correct

(\frac{x - |x|}{2})^2

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Explanation

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Official Explanation

Official

For

x ≥ 0

, we have

|x| = x

. Thus, we can substitute

|x|

with

x

in each expression.

A.

x|x| = x^2

x + |x| = 2x

2x^2 - x|x| = 2x^2 - x^2 = x^2

\frac{1}{4}(x + |x|)^2 = \frac{1}{4}(2x)^2 = x^2

(\frac{x - |x|}{2})^2 = 0

.

For

x < 0

, we replace

|x|

with

(-x)

and evaluate each expression.…

Comments

SatvikOct 7, 2024

Love how you solved this

HoughMay 4, 2024

pls explain more?

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.