If [10]y^10 = -y, and [5]y^5 \geq -y, then wh… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

If $\sqrt[10]{y^{10}} = -y$ , and $\sqrt[5]{y^{5}} \geq -y$ , then which of the following gives all possible values of y?

Correct answer marked below

-1 < y < 1

y \geq 0

y \leq 0

y = 0

Correct

|y| \geq 0

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Explanation

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Official Explanation

Official

\sqrt[10]{y^{10}} = -y

The value of

\sqrt[10]{y^{10}}

is non-negative. Hence, we can infer that

y \leq 0

\sqrt[5]{y^{5}} \geq -y

Assume y is positive:

\sqrt[5]{y^{5}}

is positive while

-y

is negative. Hence, the inequality holds.…

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What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.