December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Jan 2016
Posts: 66
Location: India
GPA: 3.01

What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
Updated on: 16 Jun 2017, 00:35
Question Stats:
61% (00:44) correct 39% (00:46) wrong based on 254 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sriamlan on 15 Jun 2017, 23:55.
Last edited by Bunuel on 16 Jun 2017, 00:35, edited 1 time in total.
Renamed the topic.




Director
Joined: 04 Dec 2015
Posts: 734
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
16 Jun 2017, 00:03
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.Answer (A)...




Manager
Joined: 26 Jan 2016
Posts: 66
Location: India
GPA: 3.01

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
15 Jun 2017, 23:58
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?



Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1375
Location: Viet Nam

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
16 Jun 2017, 00:45



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4285
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
16 Jun 2017, 08:23
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 )



Manager
Status: Preparing
Joined: 05 May 2016
Posts: 56
Location: India
Concentration: International Business, Finance

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
05 Jul 2017, 10:45
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.



Manager
Joined: 24 Jun 2017
Posts: 122

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
04 Sep 2017, 16:08
6 = 3 * 2 11^452 = (11^256)*(11^256) a^(p1)/p = 1 mod p
11^(31)/3 = 11^2 = 1 mod 3 11^256= 11^(2*128) = 1 mod 3 (11^256)/2 = 1 mod 2
together 1



Intern
Joined: 19 Aug 2017
Posts: 3

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
19 Sep 2017, 03:36
Rem11^452/6 is equivalent to Rem5^452/6
Now rem5^2/6 = 1
So Rem5^452/6 = Rem(5^2)^226/6
=> 1^226 = 1
Final Remainder = 1



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 272

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
28 Sep 2017, 13:33
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



Intern
Joined: 25 Mar 2018
Posts: 13
Location: India
Concentration: Leadership, Strategy
WE: Analyst (Energy and Utilities)

Re: What is the remainder when 11^452 is divided by 6
[#permalink]
Show Tags
26 Nov 2018, 20:30
sriamlan wrote: What is the remainder when \(11^{452}\) is divided by 6.
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 This problem is pretty simple. because if we divide 11 with 6 , we get remainder as 1 , final remainder will be (1)*452 , which is 1. if exponent had been odd say 1999, the remainder would have been 1. you can ask what if dividend doesnt go by divisor without 1 or 1 as remainder, The thing is first we try use the exponent to make the divisor to take form of (divisor*K + 1) or (Divisor*K  1), easy and medium questions fall to this category. However for hard questions we need to use cyclicity.




Re: What is the remainder when 11^452 is divided by 6 &nbs
[#permalink]
26 Nov 2018, 20:30






