Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #9


x and m are positive numbers and m

x and m are positive numbers and m is a multiple of 3. Quantity A : x/x Quantity B : x Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

4 Explanations


Isaac Silberstein

The question stem explicitly states, "x and m are positive numbers." How am I to know in this case, then, that x is an integer, as Chris mentions in the video? Why do we assume "positive number" for x means a counting number, not a positive decimal or fraction for x?

Nov 2, 2016 • Comment

Sam Kinsman, Magoosh Tutor

Hi Isaac, that's a good question! You're right that we don't know for sure whether x is an integer or not. I think that Chris mean to say that "x and m are positive numbers" in the video!

Note, though, that m has to be an integer. It is a multiple of 3, so it could be 3, 6, 9, 12, etc. All of these are integers. So we know that m is an integer.

For m, it is not entirely clear if it is an integer. However, note that this doesn't make the problem more difficult. As Chris shows in the video, if m = 3, Column A (x^m / x^3) is equal to 1. This is true for any value of x.

So if m = 3, Column A is 1. And Column B would become x^1. Since x can be any value, we don't know if x is equal to or greater than 1.

Again, all of this is true regardless of whether x has to be an integer or not. The fact that x can be any positive number doesn't change things.

I hope this helps! :)

Nov 2, 2016 • Reply


Anthony Nwodo

I solved this slightly differently, is this valid?

X^M -X^3 = M-3 vs M/3 and just tried different numbers to show that when you get to higher multiples of M, a becomes greater.

Jan 1, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

For this question, it's important to keep in mind that we're comparing the whole expression, and not just the power to which x is raised. For that reason, while it is ok to plug in values to solve this problem (which is what Chris does in the explanation video), one key observation is that when m=3, then

x^m/x^3 = x^(3-3) = x^0 = 1


x^(m/3) = x^(3/3) = x^1

Since we don't know the value of x, only that it is a positive integer, x could be equal to 1, in which case A and B would be equal. However, if x were equal to another positive integer, such as 2, then A > B. Since A could be equal to or greater than B, the answer is D, the relationship cannot be determined.

Hope this helps :)

Jan 3, 2016 • Reply


Newaz Sharif

I think this problem will be at number 8 not at number 9.

Nov 4, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Thanks for noticing this, Tuhin! You're completely right. I've made a note to our content editors that this question and video correspond to #8 of the OG, so that this can be fixed :) Thanks again!

Nov 11, 2015 • Reply


Gravatar Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

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