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Question

# What is the cube root of w?(1) The 5th root of w is 64.(2) The 15th root of w is 4.

A
Statement I alone is sufficient to answer the problem.
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B
Statement II alone is sufficient to answer the problem.
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C
Statement I and II both are needed.
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D
Either of the statements I or II is sufficient.
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E
Statement I and II both are not sufficient.
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Solution

## The correct option is D Either of the statements I or II is sufficient.Arithmetic Operations with radical expressionsDetermine the cube root of w, or determine the value of w13.(1) Given the 5th root of w is 64, then w15=64and (w15)53=6453. Since (w15)53=w(15)(53)=w13, then w13=(6453)=(6453)5=45; SUFFICIENT.(2) Given the 15th root of w is 4, then w115=4 and (w115)5=45. Since (w115)5=w515=w13, then w13=45; SUFFICIENT.The correct answer is D; each statement alone is sufficient.

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