numbers

Hi vaibhav101,

We're told that 5^A is a FACTOR of N! and the greatest integer value of A is 6. We're asked for the largest possible value of B such that 7^B is a factor of N!

This question is based on Prime Factorization, but comes with a 'twist.' We're limited by the 5s that appear in N! 5^6 allows for six 5s - and those 5s would be found in 5, 10, 15, 20 and 25 (note that 25 = 5^2, so that counts as two 5s), so we can't have any larger multiples of 5 in N! The 'twist' is that N! can actually be bigger than 25!, since 26!, 27!, 28! and 29! all have just six 5s (the same as 25!). We cannot use 30! though - since that would create a seventh 5 (which is not allowed).

We would be able to find 7s in 7, 14, 21 AND 28 (assuming that N! was either 28! or 29!), so the largest possible value of B would be 4.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich