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# Given n is a prime number, how many trailing zeroes are in the digit o

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Director
Joined: 23 Feb 2015
Posts: 922
GMAT 1: 720 Q49 V40
Given n is a prime number, how many trailing zeroes are in the digit o  [#permalink]

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22 Apr 2019, 12:13
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40% (01:21) correct 60% (00:37) wrong based on 15 sessions

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Given n is a prime number, how many trailing zeroes are in the digit of n! ?
1) n! is divisible by 25
2) n! is not divisible by 125

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Intern
Joined: 16 Sep 2018
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Given n is a prime number, how many trailing zeroes are in the digit o  [#permalink]

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22 Apr 2019, 18:45
I think it's 'C' and the number of trailing zeroes in n! should be 2.
Manager
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Re: Given n is a prime number, how many trailing zeroes are in the digit o  [#permalink]

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23 Apr 2019, 02:49
1
We can find the number of trailing zeros of n! by knowing the number of 5's in n!

Using only statement 1
1) if n! is divisible by 25, it has at least two 5's. This tells us that the number of 0's >= 2. Possible values are 2,3,4,5,6.........
INSUFFICIENT

Using only statement 2
2) if n! is not divisible by 125, then it has fewer than three 5's. This tells us that the number of 0's < 3. Possible values are only 0,1,2
INSUFFICIENT

Combining statements 1 and 2: The only common value is 2.
SUFFICIENT
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Re: Given n is a prime number, how many trailing zeroes are in the digit o  [#permalink]

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23 Apr 2019, 03:06
1
Given n is a prime number, how many trailing zeroes are in the digit of n! ?
1) n! is divisible by 25
2) n! is not divisible by 125

1) First statement says n! is having minimum two 5. It can be any prime such as 11!, 13!, 17!------------ Not sufficient
2) Second says n! is not having three 5 so it can not be divided by 125....It may be anything below prime 17! such as 13!, 11!, 7!, 5!, 3! ---------Not Sufficient.

Combining 1 and 2

n! factorial would be 11! or 13! ...

Both the choices give only two trailing zeroes.... So the answer is "C"
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Re: Given n is a prime number, how many trailing zeroes are in the digit o   [#permalink] 23 Apr 2019, 03:06
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