Determine the product of all the solutions fo… | GMAT Sprint

Free Practice Question

PS · Problem Solving

555-605

Absolute Values/Modules

Determine the product of all the solutions for the equation $(x - 3)^2 = |x - 3|$ .

Answer Choices

Correct answer marked below

-24

-15

Correct

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Explanation

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Official Explanation

Official

To solve the equation

(x - 3)^2 = |x - 3|

, we first consider two cases based on the definition of absolute value.

For the case where

x - 3 ≥ 0

, we have

(x - 3)^2 = x - 3

.

Rearranging gives us

(x - 3)^2 - (x - 3) = 0

, or

(x - 3)((x - 3) - 1) = 0

, leading to roots

x = 3

and

x = 4

. For the case where

x - 3 < 0

, we have

(x - 3)^2 = -(x - 3)

.…

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Comments

HunterJul 5, 2024

taking my GMAT next month, this helps!

NoahMay 31, 2024

thankss

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.

Determine the product of all the solutions for the equation (x−3)2=∣x−3∣(x - 3)^2 = |x - 3|(x−3)2=∣x−3∣.