It is currently 22 Sep 2017, 06:44

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What will be the remainder when 13^36 is divided by 2196?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 01 Nov 2015
Posts: 21

Kudos [?]: 21 [0], given: 28

Reviews Badge
What will be the remainder when 13^36 is divided by 2196? [#permalink]

Show Tags

New post 08 Jun 2016, 19:39
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:58) correct 42% (02:17) wrong based on 128 sessions

HideShow timer Statistics

What will be the remainder when 13^36 is divided by 2196?

A) 0
B) 1
C) 12
D) 2195
E) 5
[Reveal] Spoiler: OA

Kudos [?]: 21 [0], given: 28

Expert Post
2 KUDOS received
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4911

Kudos [?]: 5231 [2], given: 112

Re: What will be the remainder when 13^36 is divided by 2196? [#permalink]

Show Tags

New post 08 Jun 2016, 19:49
2
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
aayushagrawal wrote:
What will be the remainder when 13^36 is divided by 2196?

A) 0
B) 1
C)12
D) 2195
E) 5


"Please hit +kudos if you like this post" :-D



In such Qs, best is to get the dividend and divisor in some friendly figures..
\(13^{36} = (13^3)^{12} = 2197^{12} = (2196+1)^{12}\).....
when \((2196+1)^{12}\) is divided by 2196, all terms in the expansion are divisible by 2196 except 1^12, so the remainder will be 1
B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5231 [2], given: 112

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17592

Kudos [?]: 270 [0], given: 0

Premium Member
Re: What will be the remainder when 13^36 is divided by 2196? [#permalink]

Show Tags

New post 28 Jul 2017, 18:05
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 103

Kudos [?]: 5 [0], given: 34

Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: What will be the remainder when 13^36 is divided by 2196? [#permalink]

Show Tags

New post 20 Aug 2017, 20:28
1
This post was
BOOKMARKED
We can also use cyclicity of the last digit to answer this question
13ˆ36/2196
The remainder will depend on the last digit of Numerator ie on 3.
Cyclicity of 3 is 4 and the last digits are
3¹=3
3²=9
3³=27
3⁴=81
Now 36/4=9 the digit will have 9 full cycles and the end of the cycle has 1 as the last digit
1³⁶/2196 the reminder will be 1

Kudos [?]: 5 [0], given: 34

Manager
Manager
avatar
B
Joined: 24 Jun 2017
Posts: 77

Kudos [?]: 13 [0], given: 120

Re: What will be the remainder when 13^36 is divided by 2196? [#permalink]

Show Tags

New post 04 Sep 2017, 17:38
1
This post was
BOOKMARKED
it can be resolved on the fly via cyclicity approach by creating a pattern:
Rem[13^1 / 2196] = Rem [13 / 2196] =13
Rem[13^2 / 2196] = Rem [169 / 2196] =49
Rem[13^3 / 2196] = Rem [2197/ 2196] = 1
Rem[13^4 / 2196] = Rem [2197*13 / 2196] = 13

So the cycle is 3 as on the step four it started repeating the same remainder (you can ignore the 4th line for further calculations)

13^36 = 36 / 3 = 12 so it the last 3rd cycle which is 1

Kudos [?]: 13 [0], given: 120

Re: What will be the remainder when 13^36 is divided by 2196?   [#permalink] 04 Sep 2017, 17:38
    Similar topics Author Replies Last post
Similar
Topics:
18 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when (47)(49) is divided by 8? mun23 14 15 Jun 2017, 16:32
16 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when 3^243 is divided by 5? jimhughes477 19 04 Sep 2017, 16:25
72 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when 43^86 is divided by 5? Alterego 39 14 Jan 2017, 14:03
4 EXPERTS_POSTS_IN_THIS_TOPIC When n is divided by 6, the remainder is 2. What is the remainder when Bunuel 5 21 Jan 2017, 23:52
10 EXPERTS_POSTS_IN_THIS_TOPIC When n is divided by 5 the remainder is 3. What is the remainder when Bunuel 9 27 Dec 2016, 19:29
Display posts from previous: Sort by

What will be the remainder when 13^36 is divided by 2196?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.