Source: Revised GRE PDF 1st Ed. Section 5: Math; #22 (p. 79)

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# If c and d are positive integers

If c and d are positive integers and m is the greatest common factor of c and d, then m must be the greatest common factor of c and which of the following integers? c+d, 2+d, cd, 2d, d^2

### 3 Explanations

1

Kathleen M

I choose c=6; d=3; m=3. I got 3 as the GCF for both answer choices A and E. At this point would I need to pick new numbers and try again?

Jul 18, 2019 • Comment

Indeed you would! But you would only need to test A and E. For instance, try c = 8, d = 4, m = 4. In this case, E becomes 16, but the GCF of 16 and 8 is 8, not 4. So A must be the answer.

Kathleen M

I'm revisiting this problem and have another question. If you pick a smaller number for c and larger for d e.g. c=3; d=9 then it becomes impossible to answer the question? Because the GCF is always 3 in this case? You are only able to rule out B.

David Recine, Magoosh Tutor

In the specific case of c =3 and d = 9, you don't have enough info to solve the problem. However, there are different ways to set c lower than d that could get better results. For example, if c = 27 and d = 81, you can rule out everything except a. The general rule of thumb is that the larger c and d are, the easier it is to eliminate the wrong answers. If either c or d are a prime number, it's harder to eliminate all answers. Does that make sense?

1

Megashree R

I did not understand how Chris chose those numbers logically. Can you please explain further?

Sep 30, 2016 • Comment

Sam Kinsman

Hi Megashree,

To solve this problem, Chris chose the following numbers:

c=8
d=4
m=4

Chris chose these numbers because they satisfy what the question told us ("c and d are positive integers and m is the greatest common factor of c and d"), and they are relatively small, which means they are easy to work with.

Those are the two things you should think about when you're choosing numbers for variables: you should make sure that the numbers satisfy what the question tells us, and that the numbers are easy to work with. Also, you should avoid picking the numbers 1 and 0, since they tend to behave a bit differently than other numbers do.

2 Chris Lele, Magoosh Tutor

Sep 25, 2012 • Comment