Question: Power of 5

Comment on Power of 5

ammmmmmazing videos!! loved them all!!
gmat-admin's picture


Hi Brent!

I stumbled a little bit in the beginning but got to the answer eventually. My question is, in an expression like the one above, would it be fair to equate 5^(3x+1) to 5^1, even with the 4 present?(Assuming that we split 20 into 5 times 4) eg:5^(3x+1) = 5^1 *4^1
gmat-admin's picture

Yes, that's correct.
If 5^(3x+1) = 20, then we can also say that 5^(3x+1) = (5^1)(4^1)


hi brent,

so the part where multiplied powers of both sides by 1/3. that was to eliminate 3 from 3x correct?
gmat-admin's picture

That's correct.
Our goal is to determine the value of 5^(-x), so I needed a way to eliminate the 3 from 3x.


Hi Brent,

In this question:

What is the cube root of w?

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

Do we really have to solve equation 1 and 2 to get the answer? Or just by looking at the equations, we know that since the 5th and 15th root of w is given, it should be possible to find the cube root of w and both equations 1 & 2 should suffice?

I want to confirm if we have to solve this to prove it or if we can just see the statements and directly choose answer D.
gmat-admin's picture

Your reasoning is perfect.
Since we COULD determine the actual value of w from each statement, we COULD calculate the cube root of w.
In other words, we COULD answer the target question with certainty.
Here's my full solution:

Study Guide

The step-by-step Study Guide will help direct your studies and ensure that you cover everything that the GMAT tests.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Tweet about the course!

If you're enjoying this GMAT video course, help spread the word on Twitter.

Free “Question of the Day” emails!