Given that x and y are integers and |x - y| = 10, what is the minimum possible value of xy?

Answer Choices

Correct answer marked below

-10

-15

-20

-25

Correct

-30

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Explanation

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Official Explanation

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To find the minimum value of xy given |x - y| = 10, we can express y in terms of x. Let y = x + 10 or y = x - 10. Then, we can calculate xy for both cases. For y = x + 10, we have xy = x(x + 10) = x^2 + 10x. For y = x - 10, we have xy = x(x - 10) = x^2 - 10x. The minimum value…

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Comments

BookJan 18, 2025

thanks for the answer

AhmedDec 17, 2024

Tricky wording but good practice

HarshiJun 26, 2024

thanks for posting

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.