If \(d\) is a positive integer and \(f\) is the product of the first \(30\) positive integers, what is the value of \(d\)?
1) \(10^d\) is a factor of \(f\)
2) \(d > 6\)
d = 30!
f = a positive integer
1) f = k(10^d) where k is an integer
30! = k (10^d)
Since d is a positive integer, how many 10s are in 30!?
30/5 = 6
30/25 = 1
so there are seven 10s in 30! and d could be 0, 1, .......7. NSF.
2) d > 6,m so what ? nothing because we do not know the relationship between d and f. NSF..
1 & 2) Oh yeah... now we has relationship between d and f. Also we know the exact value of d i.e. 7.
Sufficient.. D = 7.
Then it is C.