GMATprep, practice test nº1. Question 11

If n is a positive interger less than 200 and 14n/60 is a positive integer, then n has how many different positive prime factors?

Answers are: 2, 3, 5, 6, 8

The correct one is 3, but I have no idea how to solve this one. Any help?

Thanks

If n is a positive interger less than 200 and 14n/60 is a positive integer, then n has how many different positive prime factors?

Answers are: 2, 3, 5, 6, 8

I believe the question is asking for the number of distinct positive prime factors

14n/60 can be simplified to 7n/30. If 7n/30 is a positive integer, then 30 must be a factor of n, as it is not a factor of 7.

The possibilities for n (given that n < 200) are 30, 60, 90, 120, 150, 180

If you test these numbers you will quickly see that they all have the same 3 distinct prime factors: 3, 2 and 5.

Hope that helps...

Nice explanation, GMATPaduan!

Thanks a lot for such great help