GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Nov 2018, 12:47

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# When 51^25 is divided by 13, the remainder obtained is:

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Sep 2018
Posts: 30
Re: When 51^25 is divided by 13, the remainder obtained is:  [#permalink]

### Show Tags

29 Oct 2018, 17:18
LM wrote:
When 51^25 is divided by 13, the remainder obtained is:

A. 12
B. 10
C. 2
D. 1
E. 0

Can be written as (52-1)^25

52 is a multiple of 13.

So the remainder is -1^25

= -1

-1 + 13 = 12

A
Intern
Joined: 04 Oct 2018
Posts: 6
Location: United States
Schools: Wharton '21
GPA: 3.91
Re: When 51^25 is divided by 13, the remainder obtained is:  [#permalink]

### Show Tags

04 Nov 2018, 08:46
Bunuel and VeritasKarishma, what do you think of this method? The way I did was fairly simple as well.

I did:

51^1 / 13 = remainder of 12
51^2 / 13 = remainder of 1

I noticed a pattern, whenever 13 was divided into an odd power of 51 the remainder is 12 and whenever divided by an even power the remainder was 1.

25 is odd, so remainder must be 12.

This has led me to conclude that this works for ALL numbers. A number to an any odd power and that number itself (power of 1) will always have the same remainder when divided by any integer.

Bunuel wrote:
LM wrote:
When 51^25 is divided by 13, the remainder obtained is:

A. 12
B. 10
C. 2
D. 1
E. 0

$$51^{25}=(52-1)^{25}$$, now if we expand this expression all terms but the last one will have $$52=13*4$$ in them, thus will leave no remainder upon division by 13, the last term will be $$(-1)^{25}=-1$$. Thus the question becomes: what is the remainder upon division -1 by 13? The answer to this question is 12: $$-1=13*(-1)+12$$.

_________________

Practice GMAT Scores:
Test 1 09/25/2018 Q40 V27 560
Test 2 10/02/2018 Q45 V30 620
Test 3 10/08/2018 Q40 V34 610
Test 4 10/13/2018 Q39 V35 620

Test Date: 12/03/2018

Re: When 51^25 is divided by 13, the remainder obtained is: &nbs [#permalink] 04 Nov 2018, 08:46

Go to page   Previous    1   2   3   4   [ 62 posts ]

Display posts from previous: Sort by