MathRevolution wrote:

[GMAT math practice question]

For a positive integer n, if \(5^n\) is a factor of 25!, but \(5^{n+1}\) is not a factor of 25!, what is the value of n?

A. 5

B. 6

C. 7

D. 8

E. 9

This question basically asks us to find the find what could be the maximum value of n OR one can say that what is the highest multiple of 5 which can divide 25! completely.

There are two ways to find the number of 5s in 25! to solve this -

1. Check factors of 5s in 25! :

5,10,15,20,25

The total number of 5s (n) are = 1 + 1+ 1 + 1 + 2 = 6

Thus n = 6, because n +1 = 7 and \(5^n+1\) would not be a factor of 25!.

2. Division method of finding the number of 5s.

25/5 = 5

5/5 = 1

Thus total 5s are = 5 + 1 = 6.

The correct answer is Option B.

_________________

Work Hard! Have Fun! Create History!