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Intern  Joined: 02 May 2012
Posts: 10
If x is a positive integer, then the least value of x for which x! is  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:07) correct 22% (01:07) wrong based on 131 sessions

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If x is a positive integer, then the least value of x for which x! is divisible by 1000 is?

A. 5
B. 9
C, 12
D. 15
E. 30

Originally posted by iNumbv on 08 Jan 2015, 08:20.
Last edited by Bunuel on 20 Jan 2019, 06:32, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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2
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iNumbv wrote:
If x is a positive integer, then the least value of x for which x! is divisible by 1000 is?

A. 5
B. 9
C, 12
D. 15
E. 30

Can someone please explain intuitively what the question is asking?

In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.

5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.

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Manager  Joined: 08 Nov 2014
Posts: 75
Location: India
GPA: 3
WE: Engineering (Manufacturing)
Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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1
Going by logic, x! must contain 1000 or its factors in it

1000= 5*2*5*2*5*2

Always in such type of questions '5' will be the limiting number. So we need three "5" in x!

And smallest factorial will be 15!, it contains 5, 10, 15 . iNumbv wrote:
If x is a positive integer, then the least value of x for which x! is divisible by 1000 is?

A. 5
B. 9
C, 12
D. 15
E. 30

Can someone please explain intuitively what the question is asking?

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"Arise, Awake and Stop not till the goal is reached"
Senior Manager  Joined: 13 Jun 2013
Posts: 266
Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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iNumbv wrote:
If x is a positive integer, then the least value of x for which x! is divisible by 1000 is?

A. 5
B. 9
C, 12
D. 15
E. 30

Can someone please explain intuitively what the question is asking?

1000= 2^3*5^3

therefore x! must have 5^3 in it. so, out of the given options only 15 and 30 remains. Also, since the question talks about the least value of x. therefore x must be 15.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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Bunuel wrote:
iNumbv wrote:
If x is a positive integer, then the least value of x for which x! is divisible by 1000 is?

A. 5
B. 9
C, 12
D. 15
E. 30

Can someone please explain intuitively what the question is asking?

In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.

5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.

For similiar questions check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.

Hope this helps.
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Intern  B
Joined: 27 Jul 2017
Posts: 47
Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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X! will be divisible by 1000 only if it has 3 trailing zeros. 1 trailing zero means there is at least one 2 and one 5 in the product. Concept - https://gmatclub.com/forum/everything-a ... 85592.html

Now, 5 has one trailing zero, 10 has two trailing zeros and 15 has three trailing zeros. So the answer is D.
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Non-Human User Joined: 09 Sep 2013
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Re: If x is a positive integer, then the least value of x for which x! is  [#permalink]

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_________________ Re: If x is a positive integer, then the least value of x for which x! is   [#permalink] 02 Sep 2019, 22:48
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