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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:19) correct
44%
(02:50)
wrong
based on 254
sessions
History
Date
Time
Result
Not Attempted Yet
Find the number of zeroes in 1142! × 348! × 17!.
(A) 369
(B) 370
(C) 371
(D) 375
(E) 385
(A) 369
(B) 370
(C) 371
(D) 375
(E) 385
27 Jan 2017, 03:12
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saswata4s
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..
27 Jan 2017, 03:57
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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
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 [ 10.04 KiB | Viewed 21188 times ]
