Calculate the area of the region defined by t… | GMAT Sprint

Free Practice Question

PS · Problem Solving

605-655

Absolute Values/Modules

Calculate the area of the region defined by the equation $4|x| + 2|y| = 12$ .

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Explanation

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Official Explanation

Official

To find the area of the region enclosed by the equation

4|x| + 2|y| = 12

, we first rewrite it in the form of a polygon. The vertices can be found by setting each variable to zero in turn. Setting

y = 0

gives

4|x| = 12

, leading to

|x| = 3

, so the points are (3, 0) and (-3, 0). Setting

x = 0

gives

2|y| = 12

, leading to

|y| = 6

, so the points are (0, 6) and (0, -6). The vertices…

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Comments

JoséApr 3, 2025

Can someone explain it other way?

MuhammadJul 28, 2024

thankss

MadhavFeb 17, 2024

appreciated!

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.

Calculate the area of the region defined by the equation 4∣x∣+2∣y∣=124|x| + 2|y| = 124∣x∣+2∣y∣=12.