What is the cube root of w?

[BTGmoderatorDC]

What is the cube root of w?

(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

OA D

Source: Official Guide

[Jay@ManhattanReview]

What is the cube root of w?

(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

OA D

Source: Official Guide

Let's take each statement one by one.

(1) The 5th root of w is 64.

=> w^(1/5) = 64
w = (64)^5
=> w^(1/3) = (64)^5 = [(64)^5]^(1/3) = (64)^(5/3) = A unqiue value

Sufficient.

(2) The 15th root of w is 4.

=> w^(1/15) = 4
w = (4)^(15)
=> w^(1/3) = (4)^(15) = [(4)^(15)]^(1/3) = 4^5 = A unqiue value

Sufficient.

The correct answer: D

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

What is the cube root of w?

(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

OA D

Source: Official Guide

Target question: What is the cube root of w?

Statement 1: The 5th root of w is 64.
ASIDE: If the square root of x = 7, then x = 7²
If the cube root of x = 10, then x = 10³
If the fourth root of x = 6, then x = 6⁴
etc
So, if the 5th root of w is 64, then w = 64⁵
Since we COULD determine the actual value of w, we COULD find the cube root of w
In other words, we have all of the information we need to answer the target question with certainty
Statement 1 is SUFFICIENT

Statement 2: The 15th root of w is 4
From this we can conclude that w = 4¹⁵
Since we COULD determine the actual value of w, we COULD find the cube root of w
In other words, we have all of the information we need to answer the target question with certainty
Statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent