Hi All,

We're asked for the cube root of W. This is a great example of a 'concept question' - meaning that you don't actually have to do any math to get the answer as long as you understand the concept(s) involved.

The concepts tested here are all about 'roots' of numbers. The root ultimately depends on the original number and the number-of-the-root. For example:
-The square root of 25 = +5 only (no 'negative root' applies when the root is an EVEN number - re: the square root, the 4th root, the 6th root, etc.).

-Odd-numbered roots have JUST ONE solution:
The cube root of 27 = +3 only... since (3)(3)(3) = 27
The cube root of -64 = -4 only... since (-4)(-4)(-4) = -64

-The fourth root of 16 = +2 only (again, no 'negative root' applies when the root is an EVEN number).

With all of that knowledge, you can quickly deal with the two Facts...

1) The 5th root of W is 64

Since we're dealing with a positive number and an ODD root, there is ONLY ONE answer.
Fact 1 is SUFFICIENT.

2.) The 15th root of W is 4
With Fact 2, we're also dealing with a positive number and an ODD root, there is ONLY ONE answer.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

ejager wrote:What is the cube root of w?
1. the 5th root of w is 64
2. the 15th root of w is 4

We need to determine the cube root of w. Thus, if we have a value for w, we can determine the value of the cube root of w.

Statement One Alone:

The 5th root of w is 64.

w^(1/5) = 64

w = 64^5

Since we know that we have a unique value for w, we can stop here. This is enough information to enable us to determine the value of the cube root of w. Statement one provides enough information to answer the question.

Statement Two Alone:

The 15th root of w is 4.

w^(1/15) = 4

w = 4^15

Since we know that we have a unique value for w, we can stop here. This is enough information to enable us to determine the value of the cube root of w. Statement two is also sufficient.

Answer: D