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# If n is a positive integer and the product of all integers

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Intern
Joined: 08 Mar 2009
Posts: 25
Followers: 1

Kudos [?]: 14 [0], given: 13

If n is a positive integer and the product of all integers [#permalink]  07 Nov 2009, 10:02
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Question Stats:

80% (01:40) correct 20% (01:38) wrong based on 5 sessions
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A. 10
B. 11
C. 12
D. 13
E. 14
[Reveal] Spoiler: OA

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multiple.docx [45.86 KiB]

Math Expert
Joined: 02 Sep 2009
Posts: 27535
Followers: 4327

Kudos [?]: 42593 [0], given: 6050

Re: If n is a positive number Gmat prep [#permalink]  07 Nov 2009, 12:18
Expert's post
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A. 10
B. 11
C. 12
D. 13
E. 14

$$990=2*5*3^2*11$$

We are told that $$n!=990*k=2*5*3^2*11*k$$ which means that n! must have all factors of 990 to be the multiple of 990, hence must have 11 too, so the least value of n is 11 (notice that 11! will have all other factors of 990 as well, otherwise the least value of n would have been larger).

_________________
Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 552
Location: United Kingdom
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 22

Kudos [?]: 1052 [0], given: 217

If n is a positive [#permalink]  12 Dec 2011, 05:47
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

Guys - any idea how to solve this questions? OA is not provided unfortunately.
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E.

MGMAT 1 --> 530
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Manager
Joined: 12 Jul 2011
Posts: 153
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37
WE: Engineering (Telecommunications)
Followers: 0

Kudos [?]: 21 [0], given: 42

Re: Multiple of 990 [#permalink]  12 Dec 2011, 06:55
is it 11 ?
990 = 2 * 5 * 9 * 11
so the least value for "N" can be 11.
Manager
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 33 [0], given: 12

Re: Multiple of 990 [#permalink]  12 Dec 2011, 22:12
990= 11*10*9

since 11 is a prime no which does not have factor apart from 11 and 1. so 11 is necessary no for 990.

hence n=11
Re: Multiple of 990   [#permalink] 12 Dec 2011, 22:12
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