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

Redeem

remainder problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
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 » Sun Sep 25, 2016 7:02 am
aarzoo wrote:What is the remainder when 7^7 is divided by 19?
Ho do I solve this one?
Two questions:
1) Where are the 5 answer choices that always accompany GMAT questions?
2) What is the source of this question?

Unless I'm missing something, this question really isn't a GMAT-quality question, since it requires too much number crunching (e.g., looking for a pattern by finding the remainder when 7^2, 7^3 and 7^4 are divided by 19)

We could use some modular arithmetic (https://en.wikipedia.org/wiki/Modular_arithmetic) to solve this, but I believe this would be out of scope for the GMAT.


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Sep 29, 2016 7:26 pm
I'd use some smaller powers to help you.

7� = 7³ * 7³ * 7

Now look for powers of 19 close to these. 7³ = 343, and 19² = 361, so those are good candidates. Notice that 361 - 19 = 342, so 343 / 342 has remainder 1. Thus 7³ has remainder 1 by 19, and

7� = 7³ * 7³ * 7 = (remainder 1) * (remainder 1) * (remainder 7) = remainder 7.
Top
Post new topic Post Reply
• Page 1 of 1