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

It is currently 19 Dec 2018, 07:57

TODAY:

MIT Sloan R1 Decisions - Join MIT Chat for Live Updates | Chat with UCLA Anderson Adcom @9am PT | Chat with Yale SOM R1 Admit 10am PT


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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     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!
  • Key Strategies to Master GMAT SC

     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.

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

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

Hide Tags

Manager
Manager
avatar
S
Joined: 26 Jan 2016
Posts: 66
Location: India
GMAT 1: 690 Q49 V36
GPA: 3.01
Reviews Badge
What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post Updated on: 16 Jun 2017, 00:35
1
15
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

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

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.
Most Helpful Community Reply
Director
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 734
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 16 Jun 2017, 00:03
1
5
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)...
General Discussion
Manager
Manager
avatar
S
Joined: 26 Jan 2016
Posts: 66
Location: India
GMAT 1: 690 Q49 V36
GPA: 3.01
Reviews Badge
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 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
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1375
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 16 Jun 2017, 00:45
1
1
sriamlan wrote:
What is the remainder when \(11^{452}\) is divided by 6.

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


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

The answer is A.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4285
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 16 Jun 2017, 08:23
2
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
Manager
avatar
B
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

New post 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
Manager
avatar
B
Joined: 24 Jun 2017
Posts: 122
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 04 Sep 2017, 16:08
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
Intern
Intern
avatar
Joined: 19 Aug 2017
Posts: 3
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 19 Sep 2017, 03:36
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
Senior Manager
Senior Manager
User avatar
S
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

New post 28 Sep 2017, 13:33
3
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
Intern
avatar
B
Joined: 25 Mar 2018
Posts: 13
Location: India
Concentration: Leadership, Strategy
Schools: ISB '20
WE: Analyst (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: What is the remainder when 11^452 is divided by 6  [#permalink]

Show Tags

New post 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.
GMAT Club Bot
Re: What is the remainder when 11^452 is divided by 6 &nbs [#permalink] 26 Nov 2018, 20:30
Display posts from previous: Sort by

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.