Remainder Theorem

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smishrajec: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Wed May 18, 2011 9:07 pm; Location: Pune, India; GMAT Score:410

by smishrajec » Mon Apr 09, 2012 7:02 am

Find remainder when 63^2403 is divided by 29.

Please suggest me simple ways to find the answers to questions of this type.
This question reminds me a particular type of problem, but exactly have no clear idea at all.

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Source: Beat The GMAT — Problem Solving | Mon Apr 09, 2012 7:02 am

ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Mon Apr 09, 2012 10:20 am

The remainder theorem is lengthy here and yields R = 23

Will provide the solution as an attachment a little later

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shubham_k: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Sun Apr 08, 2012 5:38 am; Thanked: 20 times

by shubham_k » Mon Apr 09, 2012 10:37 am

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Mon Apr 09, 2012 11:10 am

Please find the solution. It is a bit lengthy

Attachments

Remainder Theorem Problem.pdf: Solution to the problem attached; (795.13 KiB) Downloaded 160 times

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gaurav9839: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Oct 04, 2013 6:17 am; Thanked: 1 times

by gaurav9839 » Fri Oct 04, 2013 6:21 am

ronnie1985 wrote:The remainder theorem is lengthy here and yields R = 23

Will provide the solution as an attachment a little later

You ans is wrong, ans should be 4

see the below solution

63^2403 mod 29

since 63 and 29 are co prime and 29 is prime number

hence according tom little theorem which states a^p-1/p =1 the value will reduce to 63^23/29

now 63^23 Mod 29 = 5^23 mod 29
=5* 25^23 mod 29
4 mod 29

Hence answer is 4

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Oct 04, 2013 6:25 am

Unless I'm missing something totally basic, this question is way outside the scope of the GMAT.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Oct 04, 2013 1:13 pm

Hey All,

Brent and I agree that this question (in it's current form) is not GMAT-Like at all. While you will be asked questions about exponents and you will be asked questions about remainders, said questions will NOT look like this one.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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