Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Jul 2015, 20:06
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

N is a positive integer. 36^N and 37^N are divided by 7 with

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 93 [0], given: 0

N is a positive integer. 36^N and 37^N are divided by 7 with [#permalink] New post 12 Oct 2003, 23:43
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

N is a positive integer. 36^N and 37^N are divided by 7 with some remainders. Find the smallest N when the remainders are the same. Find the next N.
CEO
CEO
avatar
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 728 [0], given: 781

Re: PS: TRIBUTE TO THE SAME REMAINDER [#permalink] New post 13 Oct 2003, 00:48
stolyar wrote:
N is a positive integer. 36^N and 37^N are divided by 7 with some remainders. Find the smallest N when the remainders are the same. Find the next N.



n=1

36^ N divided by 7 leaves remainder of 1

37^N divided by 7 leaves remainder of 2

n =2

36^ 2 divided by 7 leaves remainder of 1^2 =1

37^2 divided by 7 leaves remainder of 2^2 =4

n= 3

36^3 divided by 7 leaves remainder of 1^3 = 1
37^2 divided by 7 leaves remainder of 2^3 = 8

since 8>7 , divide 8/7 , we get remainder of 1 ...

N = 3 is the answer....


Next N

Since we already discussed a variant of this question...allow me to do this

faster.

The next highest cube of 2 that when divided by 7 leaves a remainder 1 is

2^6 = 64 ... 64/7 leaves remainder of 1.

so , Next N =6

thanks
praetorian
SVP
SVP
User avatar
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 93 [0], given: 0

 [#permalink] New post 13 Oct 2003, 01:01
agree
a very interesting math problem! where did you get an idea?
  [#permalink] 13 Oct 2003, 01:01
Display posts from previous: Sort by

N is a positive integer. 36^N and 37^N are divided by 7 with

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.