It is currently 17 Oct 2017, 17:51

### 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 June
Open Detailed Calendar

# What is the remainder when 11^452 is divided by 6

Author Message
TAGS:

### Hide Tags

Manager
Joined: 26 Jan 2016
Posts: 90

Kudos [?]: 38 [0], given: 29

Location: India
GMAT 1: 690 Q49 V36
GPA: 3.01
What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

16 Jun 2017, 00:55
9
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:43) correct 42% (00:46) wrong based on 171 sessions

### HideShow timer Statistics

What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Jun 2017, 01:35, edited 1 time in total.
Renamed the topic.

Kudos [?]: 38 [0], given: 29

Manager
Joined: 26 Jan 2016
Posts: 90

Kudos [?]: 38 [0], given: 29

Location: India
GMAT 1: 690 Q49 V36
GPA: 3.01
Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

16 Jun 2017, 00:58
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Experts my doubt here is -
The cyclicity of power of 11 when divided by 6 is 5,4,3,2,1,0

So if we divide 452 by 6 remainder is 2

So as 2 is the remainder as per the cyclicity should not 4 be the answer instead of 1?

Kudos [?]: 38 [0], given: 29

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 296 [1], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

16 Jun 2017, 01:03
1
KUDOS
4
This post was
BOOKMARKED
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

11 divided by 6 gives remainder 5.

$$11^2 = 121$$ divided by 6 gives remainder 1.

$$11^3 = 1331$$ divided by 6 gives remainder 5.

$$11^4 = 14641$$ divided by 6 gives remainder 1.

Therefore it has a cycle of 2 with 5 and 1 as remainders.

Even powers of 11 divided by 6 gives remainder 1. And Odd powers of 11 divided by 6 gives remainder 5.

452 divided by 2 = 226.

Therefore $$11^{452}$$ divided by 6 will give remainder 1.

Kudos [?]: 296 [1], given: 261

VP
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1178

Kudos [?]: 878 [0], given: 53

Location: Viet Nam
Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

16 Jun 2017, 01:45
2
This post was
BOOKMARKED
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

$$\frac{11}{6}=\frac{5}{6} \implies \frac{11^{452}}{6}=\frac{5^{452}}{6}=\frac{(-1)^{452}}{6}=\frac{1}{6}$$

_________________

Kudos [?]: 878 [0], given: 53

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1085 [2], given: 325

Location: India
GPA: 3.5
What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

16 Jun 2017, 09:23
2
KUDOS
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

$$\frac{11}{6}$$ = Remainder $$5$$
$$\frac{11^2}{6}$$ = Remainder $$1$$

Now, $$11^{452}$$ = $$11^{2*226}$$

$$\frac{11^{2*226}}{6}$$ will leave a remainder 1

Thus, the correct answer will be (A) 1
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1085 [2], given: 325

Manager
Status: Preparing
Joined: 05 May 2016
Posts: 63

Kudos [?]: 11 [0], given: 149

Location: India
Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

05 Jul 2017, 11:45
sriamlan wrote:
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Experts my doubt here is -
The cyclicity of power of 11 when divided by 6 is 5,4,3,2,1,0

So if we divide 452 by 6 remainder is 2

So as 2 is the remainder as per the cyclicity should not 4 be the answer instead of 1?

Not sure if i can clear your doubt. You can look at the problem like when 11/6 then remainder is 5, when 11^2/6 then remainder is 1.
Now you have 11^452 which is 11^even power so remainder will be 1.

Kudos [?]: 11 [0], given: 149

Manager
Joined: 24 Jun 2017
Posts: 91

Kudos [?]: 13 [0], given: 123

Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

04 Sep 2017, 17:08
6 = 3 * 2
11^452 = (11^256)*(11^256)
a^(p-1)/p = 1 mod p

11^(3-1)/3 = 11^2 = 1 mod 3
11^256= 11^(2*128) = 1 mod 3
(11^256)/2 = 1 mod 2

together 1

Kudos [?]: 13 [0], given: 123

Intern
Joined: 19 Aug 2017
Posts: 3

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

Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

19 Sep 2017, 04:36
Rem|11^452/6| is equivalent to Rem|5^452/6|

Now rem|5^2/6| = 1

So Rem|5^452/6| = Rem|(5^2)^226/6|

=> 1^226 = 1

Final Remainder = 1

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

Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 168

Kudos [?]: 13 [2], given: 400

Re: What is the remainder when 11^452 is divided by 6 [#permalink]

### Show Tags

28 Sep 2017, 14:33
2
KUDOS
sriamlan wrote:
What is the remainder when $$11^{452}$$ is divided by 6.

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

the easiest way ever

(12 - 1)^452
___________
6
now as, 12/6 leaves no remainder
(-1)^ 452
________
6

=1/6
leaves remainder 1

cheers through the kudos button if this helps

Kudos [?]: 13 [2], given: 400

Re: What is the remainder when 11^452 is divided by 6   [#permalink] 28 Sep 2017, 14:33
Display posts from previous: Sort by