A is the product of the first 100 multiples of 8. : Problem Solving (PS)

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

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A is the product of the first 100 multiples of 8. [#permalink]

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29 Sep 2018, 18:18

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Difficulty:

55% (hard)

Question Stats:

56% (01:47) correct

44% (02:24) wrong

based on 37 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

Spoiler: OA

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

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29 Sep 2018, 18:43

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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: A is the product of the first 100 multiples of 8. [#permalink]

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29 Sep 2018, 19:48

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