x and m are positive numbers and m

David Recine, Magoosh Tutor

We can't really assume that here, because the problem says that m is positive, and 0 isn't a positive number. Without the "m is positive" constraint, though, we could. That would be a significantly different math problem then, wouldn't it? ;)

Sep 2, 2018 • Reply

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

Emma Muhleman

So ETS essentially answered their own question wrong, no? Shouldn't we report this?

Feb 1, 2018 • Reply

David Recine, Magoosh Tutor

ETS answered the question correctly. The answer really is "(D) the relationship cannot be determined from the information given."

The only error here is on the part of Magoosh-- Chris shouldn't have said that x is an integer. However, this is a minor error, as the ETS question would still have the same answer even if we knew that x *was* an integer. It doesn't actually matter if x is an integer or not, since the answer depends only on the minimum value of m, which is 3.

This is reflected both in Chris's video explanation and ETS's official text explanation on pages 402-403 of the OG.

Feb 6, 2018 • Reply

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

and

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

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