990

Expert replies

B166418: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Sat Mar 26, 2011 4:59 am; Thanked: 4 times

by B166418 » Wed Jun 29, 2011 10:50 am

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

A 10
B 11
C 12
D 13
E 14

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 29, 2011 10:50 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 29, 2011 10:53 am

Hi,
990 = 9*10*11
11 is a prime number so we need n! to be at least 11! to be divisible by 990.

Hence, B

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Wed Jun 29, 2011 12:12 pm

Hey Frankenstine, where do 7 and 8 divide 990 with no remainder?
And if this is not the question wants then why haven't u selected 10 as the least possible value?

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 30, 2011 2:28 am

winniethepooh wrote:Hey Frankenstine, where do 7 and 8 divide 990 with no remainder?
And if this is not the question wants then why haven't u selected 10 as the least possible value?

Hi,
I think you have misinterpreted the question. What the question says is:
Find the least value of n such that 990 is a factor of n!.
990 = 2*3^2*5*11
Now for 990 to be a factor of n!, 11 should be a factor of n!. The least value of n that satisfies this condition is 11.
Consider 10! = 1.2.3...10
11 is not a factor of this right?

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Thu Jun 30, 2011 2:44 am

990 = 11*10*9
thus 11!.
B it is.

For Understanding Sustainability,Green Businesses and Social Entrepreneurship visit -https://aamthoughts.blocked/
(Featured Best Green Site Worldwide-https://bloggers.com/green/popular/page2)

Like this post

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Thu Jun 30, 2011 6:32 am

Thanks Frankenstine!

Like this post

Buix0065: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Mon Jan 10, 2011 4:54 pm; Thanked: 1 times

by Buix0065 » Fri Jul 01, 2011 2:43 pm

Frankenstein wrote:
winniethepooh wrote:Hey Frankenstine, where do 7 and 8 divide 990 with no remainder?
And if this is not the question wants then why haven't u selected 10 as the least possible value?
Hi,
I think you have misinterpreted the question. What the question says is:
Find the least value of n such that 990 is a factor of n!.
990 = 2*3^2*5*11
Now for 990 to be a factor of n!, 11 should be a factor of n!. The least value of n that satisfies this condition is 11.
Consider 10! = 1.2.3...10
11 is not a factor of this right?

Hi Frankenstein,

Just to make sure I understand your reasoning.

1. a number is a factor if all primes pair
2. 990 has 2, 5, and 11 that need to pair
3. the smallest that n can be to ensure n! will pair 2, 5, 11 is 11?

Thanks for your insights!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review