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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: 22

Kudos [?]: 59 [0], given: 13

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

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07 Nov 2009, 11:02
00:00

Difficulty:

15% (low)

Question Stats:

89% (00:45) correct 11% (00:52) wrong based on 28 sessions

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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]

Kudos [?]: 59 [0], given: 13

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132499 [0], given: 12323

Re: If n is a positive number Gmat prep [#permalink]

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07 Nov 2009, 13:18
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).

_________________

Kudos [?]: 132499 [0], given: 12323

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 533

Kudos [?]: 4208 [0], given: 217

Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If n is a positive [#permalink]

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12 Dec 2011, 06:47
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.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Kudos [?]: 4208 [0], given: 217

Manager
Joined: 13 Jul 2011
Posts: 140

Kudos [?]: 52 [0], given: 42

Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37
WE: Engineering (Telecommunications)

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12 Dec 2011, 07:55
is it 11 ?
990 = 2 * 5 * 9 * 11
so the least value for "N" can be 11.

Kudos [?]: 52 [0], given: 42

Manager
Joined: 26 Apr 2011
Posts: 225

Kudos [?]: 22 [0], given: 14

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12 Dec 2011, 23:12
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

Kudos [?]: 22 [0], given: 14

Re: Multiple of 990   [#permalink] 12 Dec 2011, 23:12
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