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# What is the least value for n?

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SVP
Joined: 21 Jul 2006
Posts: 1510
What is the least value for n? [#permalink]

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23 Aug 2009, 02:08
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80% (01:40) correct 20% (02:39) wrong based on 17 sessions

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If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?

A. 8

B. 9

C. 10

D. 11

E. 12
Senior Manager
Joined: 27 May 2009
Posts: 268
Re: What is the least value for n? [#permalink]

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23 Aug 2009, 02:24
1
KUDOS
IMO D: ques says n!. divisible by 990 or 11*10*9
Senior Manager
Joined: 27 May 2009
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 13:30
1
KUDOS
bhanushalinikhil wrote:
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.

See, here the factors of 990 = 3*3*2*5*11...

Now this divides n..... so we need to have all these factores ie. 2,3,5,11 ..then only it will divide..in n...

in n! .. the max should have 11 ....

Hope its clear now
Manager
Joined: 28 Jul 2009
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Location: India
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Re: What is the least value for n? [#permalink]

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24 Aug 2009, 05:02
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.
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Manager
Joined: 18 Jul 2009
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Location: India
Schools: South Asian B-schools
Re: What is the least value for n? [#permalink]

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24 Aug 2009, 08:45
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given that 990a = n! (whr a is multiple of 990)

now 990 = 3*3*2*5*11.......hence max value is 11..OA D
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Manager
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Re: What is the least value for n? [#permalink]

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24 Aug 2009, 21:44
rohansherry wrote:
bhanushalinikhil wrote:
rohansherry wrote:
IMO D: ques says n!. divisible by 990 or 11*10*9

Could you please elaborate? I didn't quite get it.

See, here the factors of 990 = 3*3*2*5*11...

Now this divides n..... so we need to have all these factores ie. 2,3,5,11 ..then only it will divide..in n...

in n! .. the max should have 11 ....

Hope its clear now

Thanks. This is clear. I never understood the question in the first place.
+1 for you.
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Director
Joined: 25 Oct 2008
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Re: What is the least value for n? [#permalink]

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28 Sep 2009, 19:48
I am not too sure i got this one..
990=11 x 3 x 3 x 5 x 2..ok..
So since we want the MINIMUM value of n we didide this by the MAXIMUM prime factor which is 11?
Am i understanding it correctly??
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Re: What is the least value for n?   [#permalink] 28 Sep 2009, 19:48
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