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

Redeem

The Powers that'll be

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 71
Joined: Sun Feb 21, 2010 9:16 pm
Thanked: 3 times
GMAT Score:750

The Powers that'll be

by ashforgmat » Mon Jan 03, 2011 1:29 am
Please can someone help me with the answer of this question ?
What is the unit's digit of the solution to :
(177)^28 - (133)^23

I know the technique just wanted to confirm the answer....
Thanks...
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Mon Jan 03, 2011 1:35 am
ashforgmat wrote:Please can someone help me with the answer of this question ?
What is the unit's digit of the solution to :
(177)^28 - (133)^23

I know the technique just wanted to confirm the answer....
Thanks...
should be 4:
7 has a 4 place cycle: 7, 9, 3, 1. Since 28 is a multiple of 4, 177^28 will end with a 1.

by the same token, 3 has a 4-place cycle: 3, 9, 7, 1. 23 is "one less than" the nearest multipe of 4, so it's in the third place of the cycle: 7.

the units digit of the difference should then be ...1 - ...7 = ...4, in the same way that 11-7 is 4.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
Post new topic Post Reply
• Page 1 of 1