Number properties

Expert replies

Previous Topic Next Topic

joinn: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Apr 13, 2011 8:52 pm

by joinn » Wed Jun 22, 2011 10:13 am

find the remainder when 3(12!)-15(11!)divides 22(11!)+22!

a) 11! b) 10! c)12! d) 9! e) 8!

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 22, 2011 10:13 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 22, 2011 10:22 am

Hi,
3(12!)-15(11!) = 3*12*11! - 15*11! = (36-15)*11! = 21*11!
[22(11!)+22!] = [(21+1)(11!)+22!] = 21*11! + 11! + 22!
22! = 11!*12*13*..*21*22 = 11!*21*(12*13...20*22)
So, 22! is divisible by 21*11!
21*11! is divisible by 22*11!
We are left with 11!

So, [(21+1)(11!)+22!] when divided by 21*11! leaves 1*11! = 11!

Hence, A

Last edited by Frankenstein on Sun Jun 26, 2011 9:35 am, edited 2 times in total.

Cheers!

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

Like this post

joinn: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Apr 13, 2011 8:52 pm

by joinn » Sat Jun 25, 2011 9:00 am

Hi Frankestein, could you please elaborate, I didn't understand from third step

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 » Sun Jun 26, 2011 9:37 am

joinn wrote:Hi Frankestein, could you please elaborate, I didn't understand from third step

Hi,
There were a couple of typos(wrote 22 instead of 21) in my previous post. I have edited my post now. If you still think it is not clear, let me know where you have problem. I will try to make it better.

Cheers!

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

Like this post

joinn: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Apr 13, 2011 8:52 pm

by joinn » Mon Jun 27, 2011 6:10 pm

yeah my doubt is from third step
when 11!*21! divides 22! then what about 22*20*19*18*17*16*15*14*13*12 aren't these also not remainders ?

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 » Mon Jun 27, 2011 8:46 pm

joinn wrote:yeah my doubt is from third step
when 11!*21! divides 22! then what about 22*20*19*18*17*16*15*14*13*12 aren't these also not remainders ?

Hi,
That is the quotient, not remainder.
Example: 16 when divided by 2 gives quotient of 8, but the remainder is zero.

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 » Mon Jun 27, 2011 10:16 pm

Wrong question accompanied with wrong answer!
Try calculating with a calculator!

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