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

It is currently 14 Sep 2014, 18:16

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

remainder

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 27 Jun 2013
Posts: 6
Followers: 0

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

remainder [#permalink] New post 01 Jul 2013, 06:13
1
This post was
BOOKMARKED
Find the remainder when 54^124 is divided by 17.

a)4
b)5
c)13
d)15



Please provide the solution with explanation.
Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4751
Location: Pune, India
Followers: 1110

Kudos [?]: 5014 [3] , given: 164

Re: remainder [#permalink] New post 01 Jul 2013, 19:31
3
This post received
KUDOS
Expert's post
SAMHITAC wrote:
Find the remainder when 54^124 is divided by 17.

a)4
b)5
c)13
d)15



Please provide the solution with explanation.


With such big numbers, the use of binomial becomes efficient. Check this post for concepts of binomial theorem for remainder questions: http://www.veritasprep.com/blog/2011/05 ... ek-in-you/

54^{124} = (51 + 3)^{124}
51 is divisible by 17 so we only have to worry about the remainder when 3^{124} is divided by 17. Look for a power of 3 which is close to 17 - we don't see a power of 3 which is one more or one less than 17 but we do have a power of 2 which is one less than 17. So if we get a power of 3 that is 1 or 2 less or more than a multiple of 17, that will work too.

3^{124} = 9^{62} = ( 17 - 8)^{62}

So now we have to worry about (-8)^{62} only

(-8)^{62} = 2^{186} = 2^2 * 16^{46} = 4*(17 - 1)^{46}

Since -1^{46} = 1, remainder will be 4*1 = 4
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: remainder   [#permalink] 01 Jul 2013, 19:31
    Similar topics Author Replies Last post
Similar
Topics:
remainder Nihit 22 23 Jul 2008, 04:34
Remainders ventivish 4 15 May 2008, 17:16
3 When x is divided by 5, the remainder is 2. Is x divisible marcodonzelli 2 27 Jan 2008, 10:32
Remainder ps_dahiya 4 05 Jul 2006, 10:38
Remainder getzgetzu 8 24 Nov 2005, 01:20
Display posts from previous: Sort by

remainder

  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®.