The answer is 3 I think.
Here's how I did it ...
n<200 and 14n/60 is an integer

(2* 7 * n)/ 2* 2* 3 * 5
= (7 * n)/ 2* 3 * 5

Now , for [(7 * n)/ 2* 3 * 5] to be an integer , n should be a multiple of 30 (denominator = 30)
number of Prime factors of 30 = 3

Note that since n< 200 , we cannot consider the next multiple of 30 which will introduce the another prime number which would be 7 because then n will become 210 and greater than 200

skalevar wrote:I'd love some additional explanation regarding the answer to the questions below, from the software simulated Practice Test available from mba.com

If n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different prime factors?
A. 2
B. 3
C. 5
D. 6
E. 8
I'm really kind of stuck on this questions, so if you have any insights, they would be much appreciated!
Thanks,

Hi skalevar,

The easiest way to approach this question is to a pick number. Since, the answer has to be a unique value this means that for any value of n ( n should be positive and less than 200), the number of different prime factors of n is same. Also, note that for this value of n, 14n/60 should be an integer. The easiest number to pick is n=60, then 14n/60= 14. Now, see 60= 2*2*3*5. Hence, 3 different prime factors. Answer B.

I would prefer debmalya_dutta's way of using Prime Factorization..its very easy..

(14n)/60=(7n)/30

n should be divisible by 30

n=30,60,90.....180

each has 3 diff prime factors