It is currently 25 Jun 2017, 19:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Mar 2009
Posts: 25
If n is a positive integer and the product of all integers [#permalink]

### Show Tags

07 Nov 2009, 11:02
00:00

Difficulty:

15% (low)

Question Stats:

87% (01:29) correct 13% (00:52) wrong based on 23 sessions

### HideShow timer Statistics

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

Attachments

multiple.docx [45.86 KiB]

Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: If n is a positive number Gmat prep [#permalink]

### Show Tags

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).

_________________
Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If n is a positive [#permalink]

### Show Tags

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

Manager
Joined: 13 Jul 2011
Posts: 144
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37
WE: Engineering (Telecommunications)

### Show Tags

12 Dec 2011, 07:55
is it 11 ?
990 = 2 * 5 * 9 * 11
so the least value for "N" can be 11.
Manager
Joined: 26 Apr 2011
Posts: 228

### Show Tags

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
Re: Multiple of 990   [#permalink] 12 Dec 2011, 23:12
Similar topics Replies Last post
Similar
Topics:
87 n is a positive integer, and k is the product of all integer 21 21 Feb 2017, 01:27
97 If the product of all the factors of a positive integer, N 30 01 Jun 2017, 12:37
119 If n is a positive integer and the product of all integers 48 08 May 2017, 11:50
19 n is a positive integer, and k is the product of all integer 15 15 May 2017, 17:30
1 If n is a positive integer and the product of all the intege 7 27 Feb 2014, 04:59
Display posts from previous: Sort by