Question: 32 and 27 with Exponents

Comment on 32 and 27 with Exponents

from 2nd step -
2^45 3^30

(2^30) (2^15) / (3^30) 1

(0.66)^30 (2^15) 1

since 0.66^30 yields to very small number, quantity A will be
smaller than 1. hence B

Is this way ok!
greenlight-admin's picture

Everything you did was correct, but that strategy could get you in trouble.

Let's start from...

Quantity A: (0.66^30)(2^15)
Quantity B: 1

I agree that 0.66^30 is a very small number. However, 2^15 is a very big number. So, what you end up with is...

Quantity A: (a very small number)(a very big number)
Quantity B: 1

How can we be sure that Quantity A is less than 1?

I used the method of unit's digits and got the same answer
greenlight-admin's picture

Can you tell us more about your solution? It sounds as though you focused solely on the units digit of each quantity.
Is that correct?


I approached sort of what Stunnerxoxo alluded to, I think. I saw the numbers and said, oh man, okay units digits stuff again. I was pretty confident that by the time I got to 7^5 the number was something-something-big-number7. I just told myself, there is no way on earth 2^5 (which equals 32) can compete with 7^5, so the answer must be B. I'm pretty sure this was the wrong way of doing it. I've been catching myself solving the problems incorrectly in all the questions until you come along and explain the material, that is when it makes a lot of sense. Love your courses!

I'm having a hard time understanding the solutions to these sorts of root questions. I haven't been able to solve most of these without clicking the video.

I'm supposed to take my test in February, but I'm no closer in progress than I was two weeks ago. Do you have any advice?
greenlight-admin's picture

This particular question is pretty tricky.

I suggest that you check out the linked questions in the Reinforcement Activities boxes of the following two videos:

The concepts/techniques involved are similar to those needed for the question.


Is there an easy way for me to know that 2^5=32? It may be simple math, but it doesn't come naturally to me. Please direct me to whatever video or module teaches how to figure out powers and roots higher than squares. I've been searching for a fast way to figure out nth roots... Still don't know.
greenlight-admin's picture

You should try to memorize all of the powers shown at 9:10 of the following video:

You can also find them here:


Hello, the approach that I applied was the following:
instead of multiplying it by 32, 9 times. I worked with 32^3 and instead 27^10 I worked with 27^4.
Is this approach applicable?
greenlight-admin's picture

It's hard for me to tell how your solution looks.
What steps are you taking to replace 32^9 with 32^3, and to replace 27^10 with 27^4?

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

QC Strategies

When you encounter a Quantitative Comparison question, be sure to consider which strategy might best apply: 


Free “Question of the Day” emails!