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Find the number of zeroes in 1142! × 348! × 17!

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Find the number of zeroes in 1142! × 348! × 17!  [#permalink]

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New post Updated on: 27 Jan 2017, 02:53
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Question Stats:

49% (01:39) correct 51% (02:10) wrong based on 85 sessions

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Find the number of zeroes in 1142! × 348! × 17!.

(A) 369
(B) 370
(C) 371
(D) 375
(E) 385

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Originally posted by saswata4s on 27 Jan 2017, 01:22.
Last edited by saswata4s on 27 Jan 2017, 02:53, edited 3 times in total.
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Re: Find the number of zeroes in 1142! × 348! × 17!  [#permalink]

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New post 27 Jan 2017, 02:12
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saswata4s wrote:
Find the number of zeroes in 1142! × 348! × 17!.

(A) 369
(B) 371
(C) 375
(D) 370
(E) 385


Hi,
Number of 0s will depend upon number of 5s..
1) number of 5s= \(\frac{1142}{5}+\frac{348}{5}+\frac{17}{5}\)=228+69+3=300..
2) number of 25s=\(\frac{1142}{25}+\frac{348}{25}+\frac{17}{25}\)=45+13=58..
3) number of 125s=\(\frac{1142}{125}+\frac{348}{125}+\frac{17}{125}\)=9+2=11..
4) number of 625s=\(\frac{1142}{625}+\frac{348}{625}+\frac{17}{625}\)=1..

Total number of 5s= 300+58+11+1=370

Ans 370..

It seems you have not put the choices in order and that is why 370 is in D choice and not B..
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Re: Find the number of zeroes in 1142! × 348! × 17!  [#permalink]

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New post 27 Jan 2017, 02:55
chetan2u wrote:
It seems you have not put the choices in order and that is why 370 is in D choice and not B..


I've updated the correct OA. Thanks for pointing out.

Cheers.
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Re: Find the number of zeroes in 1142! × 348! × 17!  [#permalink]

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New post 27 Jan 2017, 02:57
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Hi sawata4s,
To find the number of zero’s in a factorial, we get to understand, “how we get tens (zero’s) in a factorial?”
We get 10 when we have a minimum of one “2” and one “5”,
10 = 2 * 5
2’s and 5’s in a combination will give us the number of 10’s,
For every “2” in a factorial we may not have a “5”, but for every “5” in a factorial we will have “2”,
So we can just find the number of five’s to evaluate the number of zero’s
There are multiple ways to do that,
you can see the below image for solving it,
So the answer is B.
Hope this helps
Attachments

factorial.png
factorial.png [ 10.04 KiB | Viewed 1743 times ]


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Re: Find the number of zeroes in 1142! × 348! × 17!  [#permalink]

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Re: Find the number of zeroes in 1142! × 348! × 17! &nbs [#permalink] 07 Jan 2019, 10:56
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