Last visit was: 20 Jul 2024, 09:51 It is currently 20 Jul 2024, 09:51
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642522 [21]
Given Kudos: 86708
Send PM
Most Helpful Reply
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11477
Own Kudos [?]: 34468 [7]
Given Kudos: 323
Send PM
General Discussion
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5317
Own Kudos [?]: 4241 [2]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Intern
Intern
Joined: 22 Mar 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 4
Send PM
Re: What is the remainder when 52^60 is divided by 31 [#permalink]
Quote:
52 = 62 - 10

52^60mod31 = (-10)^60mod31 = 10^60mod31 = 7^30mod31 = 2^10mod31 = 1^2mod31 = 1

IMO B


Kinshook Could you please explain what you've exactly done in this part of your solution "10^60mod31 = 7^30mod31 = 2^10mod31 = 1^2mod31"? :please

I understand this part "52^60mod31 = (-10)^60mod31 = 10^60mod31" but then I would have proceded the following way: 2^60*5^60mod31 = 32^12*125^20mod31 = 1^12*1^20mod31 = 1. However, it took me too much time to come up with my solution, it seems to me that your solution is much faster and that you know some tricks in modular arithmetic that I don't know yet... :lol:
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5317
Own Kudos [?]: 4241 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: What is the remainder when 52^60 is divided by 31 [#permalink]
1
Kudos
Vendap02 wrote:
Quote:
52 = 62 - 10

52^60mod31 = (-10)^60mod31 = 10^60mod31 = 7^30mod31 = 2^10mod31 = 1^2mod31 = 1

IMO B


Kinshook Could you please explain what you've exactly done in this part of your solution "10^60mod31 = 7^30mod31 = 2^10mod31 = 1^2mod31"? :please

I understand this part "52^60mod31 = (-10)^60mod31 = 10^60mod31" but then I would have proceded the following way: 2^60*5^60mod31 = 32^12*125^20mod31 = 1^12*1^20mod31 = 1. However, it took me too much time to come up with my solution, it seems to me that your solution is much faster and that you know some tricks in modular arithmetic that I don't know yet... :lol:


Hi Vendap02
10^60mod31 = 100^30mod31 = (93+7)^30mod31 = 7^30mod31 = = 343^10mod31 = (341+2)^10mod31 = 2^10mod31 = (31+1)^2mod31 = 1^2mod31 = 1
Hope it is clear now
Intern
Intern
Joined: 22 Mar 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 4
Send PM
Re: What is the remainder when 52^60 is divided by 31 [#permalink]
Great, thank you Kinshook! :)
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34038
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: What is the remainder when 52^60 is divided by 31 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: What is the remainder when 52^60 is divided by 31 [#permalink]
Moderator:
Math Expert
94430 posts