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

 It is currently 17 Feb 2019, 08:03

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

# Remainder when 25^10 is divided by 576?

Author Message
Intern
Joined: 11 Sep 2012
Posts: 7
Remainder when 25^10 is divided by 576?  [#permalink]

### Show Tags

14 Oct 2018, 05:24
00:00

Difficulty:

(N/A)

Question Stats:

67% (02:07) correct 33% (02:03) wrong based on 3 sessions

### HideShow timer Statistics

a) 241
b) 341
c) 571
d) 680
e) None of these

Posted from my mobile device
Manager
Joined: 09 Jun 2014
Posts: 240
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Remainder when 25^10 is divided by 576?  [#permalink]

### Show Tags

14 Oct 2018, 05:42
1
asifahmed500 wrote:
a) 241
b) 341
c) 571
d) 680
e) None of these

Posted from my mobile device

We need to find out the remainder of 25^10 when divided by 576.
Please note that 576 = 24^2

Using Binomial Theorem

25^10 = (24 + 1)^10
In the expansion, there will be 11 terms where the powers of 24 will vary from 0 to 10.
If the power of 24 is greater than or equal to 2 in a term, that term will be divisible by 576
The terms that will not be divisible by 576 are the terms that have powers of 24 as 0 or 1.
Those terms are
10C1*24^1*1^9 + 10C0*24^0*1^10
= 10*24*1 + 1*1*1
= 241

So, Rem [25^10/576] = 241

Press Kudos if it helps!!
Intern
Joined: 11 Sep 2012
Posts: 7
Re: Remainder when 25^10 is divided by 576?  [#permalink]

### Show Tags

14 Oct 2018, 05:44
Is it possible to solve power of cyclicity approach

Posted from my mobile device
Re: Remainder when 25^10 is divided by 576?   [#permalink] 14 Oct 2018, 05:44
Display posts from previous: Sort by