zoom wrote:

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) \(d > 6\)

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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.