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is the largest value of integer n

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by gmatmachoman » Mon May 31, 2010 2:17 am
If P = (n)(n - 1)(n - 2) . . . (1) and n > 2, what is the largest value of integer n where P has zero as its last 6 digits and a non-zero digit for its millions place?

(A) 29
(B) 30
(C) 34
(D) 35
(E) 39
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by jube » Mon May 31, 2010 2:28 am
edit:

I didn't count the 5 in 25 twice. Taking that into account, the answer becomes A



---

Original:


I think it should be C.

6 zeros will be obtained by multiplying 2 & 5, 6 times. This means that 2 and 5 need to occur 6 times maximum in the series.

We get 6 2s with 2, 4, 6, 8.

6 5s --> 5, 10, 15, 20, 25, 30. Therefore, n *has* to be at least 30.

Since we need the biggest n, it should be 34. (35 would lead to there being 7 zeroes)
Last edited by jube on Mon May 31, 2010 4:57 am, edited 1 time in total.
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by liferocks » Mon May 31, 2010 2:37 am
p=n! and the number of 5 in P is 6
so (n/5)+(n/25)=6..1

only 29 satisfies 1

hence ans option A
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