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# A is the product of the first 100 multiples of 8.

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Senior Manager
Joined: 18 Jul 2018
Posts: 275
Location: India
Concentration: Finance, Marketing
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A is the product of the first 100 multiples of 8.  [#permalink]

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29 Sep 2018, 19:18
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Difficulty:

55% (hard)

Question Stats:

55% (01:52) correct 45% (02:21) wrong based on 31 sessions

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A is the product of the first 100 multiples of 8. How many zeros would be there at the end of A?

a) 10
b) 11
c) 12
d) 24
e) 25

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Posts: 6967
Re: A is the product of the first 100 multiples of 8.  [#permalink]

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29 Sep 2018, 19:43
Afc0892 wrote:
A is the product of the first 100 multiples of 8. How many zeros would be there at the end of A?

a) 10
b) 11
c) 12
d) 24
e) 25

So $$8*(8*2)*(8*3)*(8*4).....(8*99)(8*100)=8^{100}*(1*2*3..99*100)=8^{100}*100!$$

So zeroes would depend on numbers of 5s in 100! = $$\frac{100}{5}\frac{100}{5^2}=20+4=24$$

So D
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Re: A is the product of the first 100 multiples of 8.  [#permalink]

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29 Sep 2018, 20:48
this math problem is a common pattern in gmat.

Here, there is a minor error of the question. That is, 0 can be the multiple of 8. I believe that there should be a modification on this question.

The answer is simple itself. A = 100! * 8^100. We look for the number of factors 5 => D is the answer
Re: A is the product of the first 100 multiples of 8. &nbs [#permalink] 29 Sep 2018, 20:48
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