BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

remainders result

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

remainders result

by sanju09 » Wed May 02, 2012 4:23 am
If n = 5^50, how many different remainders result when n, n + 7, n + 11, n + 18, n + 21, n + 29, and n + 32 are each divided by 11?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7



https://www.crushthetest.com
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed May 02, 2012 7:06 am
sanju09 wrote:If n = 5^50, how many different remainders result when n, n + 7, n + 11, n + 18, n + 21, n + 29, and n + 32 are each divided by 11?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Nice question!

The first thing we should recognize is that n/11 and (n+11)/11 will have the same remainder.

Example: Let n = 20, which means n+11=31
20/11 gives us a remainder of 9
31/11 gives us a remainder of 9
Notice that 11 divides into 20 one time, with remainder 9, and 11 divides into 31 two times, with remainder 9.
Since 31 is 11 greater than 20, we can see that 11 divides into 31 one more than 11 divides into 20 and we are left with the same remainder.

Similarly, n+7, n+18 and n+29 will all have the same remainder when divided by 11
Here's why:
Let's say that (n+7)/11 gives us a quotient of q and remainder of k.
This means that 11 divides into n+7 q times with k left over.
Since n+18 is 11 more than n+7, we know that (n+18)/11 will give us a quotient of q+1 and remainder of k.
Similarly, (n+29)/11 will give us a quotient of q+2 and remainder of k.

Finally, using similar logic, we can see that n+21 and n+32 will all have the same remainder when divided by 11

So, the answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1