If -9 < m < -4 and 7 < n < 11, which of the following can be a value of [4]-mn? I. 2 II. 3 III. 4

If -9 < m < -4 and 7 < n < 11, which of the f… | GMAT Sprint

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705-805

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If $-9 < m < -4$ and $7 < n < 11$ , which of the following can be a value of $\sqrt[4]{-mn}$ ?
I. 2
II. 3
III. 4

Answer Choices

Correct answer marked below

I only

II only

Correct

III only

I and II only

II and III only

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Explanation

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Official Explanation

Official

Given

-9 < m < -4

and

7 < n < 11

, we find the range of

mn

mn

must be more than

-4 \times 7 = -28

and less than

-9 \times 11 = -99

-99 < mn < -28

Multiplying by

-1

gives:

28 < -mn < 99

Taking the fourth root:

\sqrt[4]{28} < \sqrt[4]{-mn} < \sqrt[4]{99}

Now, compare with the given numbers:…

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What this question tests

What it tests

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

Common trap

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

If −9<m<−4-9 < m < -4−9<m<−4 and 7<n<117 < n < 117<n<11, which of the following can be a value of −mn4\sqrt[4]{-mn}4−mn​?I. 2II. 3III. 4