Given the equation $m = 5 - (5 - x)^2$ , what is the maximum value of m?

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-15

-5

Correct

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Explanation

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Official Explanation

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The key to solving this problem is to analyze the function on the right side of the equation that determines the value of m. The constant 5 is being reduced by a squared expression. For any real number x, the expression (5 - x)^2 will yield a non-negative result, which means it can either be 0 or a positive value. This non-negative result is then subtracted from 5. The best scenario occurs when (5 - x)^2 equals 0, meaning that the positive value of 5 remains untouched by any…

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Comments

joaquinMar 5, 2025

taking my GMAT next month, this helps!

MadonnaMar 21, 2025

cheers!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Given the equation m=5−(5−x)2m = 5 - (5 - x)^2m=5−(5−x)2, what is the maximum value of m?