Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Aug 2014, 19:59

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the remainder of 2 ^51 divided by 7 ? What is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 67 [0], given: 39

What is the remainder of 2 ^51 divided by 7 ? What is the [#permalink] New post 07 Sep 2006, 22:20
What is the remainder of 2 ^51 divided by 7 ?

What is the remainder of 3^19 when divided by 10

a) 0
b) 1
c) 5
d) 7
e) 9

I have a question on those two exponents , i will post it after you solve it ?
Senior Manager
Senior Manager
avatar
Joined: 11 May 2006
Posts: 263
Followers: 1

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

GMAT Tests User
 [#permalink] New post 07 Sep 2006, 22:32
remainder of 2^0 / 7 = 1
2^1 / 7 = 2
2^2/ 7 = 4

and then the pattern repeats.

by this logic, remainder of 2^51/7 = 1
Senior Manager
Senior Manager
avatar
Joined: 11 May 2006
Posts: 263
Followers: 1

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

GMAT Tests User
 [#permalink] New post 07 Sep 2006, 22:43
for remainder of 3^19 / 10

unit digit of 3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 7

then the pattern repeats.
so unit digit of 3^19 = 7

hence remainder of 3^19 / 10 = 7
Manager
Manager
avatar
Joined: 30 Jun 2006
Posts: 89
Followers: 0

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 07 Sep 2006, 23:17
2 ^ 51 = 8 ^ 17 = (7 + 1) ^ 17
We needn't expand this because the 18th ( the last term ) in this expansion will be 1 and the rest of the terms will have 7 as one of the factors. Hence the remainder would be 1.


The units digit in the expansion
3 ^ 1 = 3
3 ^ 2 = 9
3 ^ 3 = 27 ( units digit 7 )
3 ^ 4 = 81 ( units digit 1 )
3 ^ 5 = 153 ( units digit 3 )
........

There is a trend in the units digits and when a number is divided by 10 then the units digit would be the remainder.

Hope this helps.
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 67 [0], given: 39

 [#permalink] New post 07 Sep 2006, 23:23
jainvik7

Very comprehensive approach... very
Manager
Manager
avatar
Joined: 30 Jun 2006
Posts: 89
Followers: 0

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 07 Sep 2006, 23:25
Thanks,
iced_tea and yezz
:-D
Director
Director
avatar
Joined: 13 Nov 2003
Posts: 801
Location: BULGARIA
Followers: 1

Kudos [?]: 19 [0], given: 0

GMAT Tests User
 [#permalink] New post 08 Sep 2006, 02:03
IMO second Q can be re-phrased as; What is the last digit of 3^19 ? It is 7 .
Current Student
User avatar
Joined: 29 Jan 2005
Posts: 5253
Followers: 23

Kudos [?]: 126 [0], given: 0

GMAT Tests User Reviews Badge
 [#permalink] New post 08 Sep 2006, 02:20
BG wrote:
IMO second Q can be re-phrased as; What is the last digit of 3^19 ? It is 7 .


Same question here. I think it is 1.
Intern
Intern
avatar
Joined: 04 May 2006
Posts: 40
Followers: 0

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

 [#permalink] New post 08 Sep 2006, 05:27
It looks like we can use this approach

2 ^ 51 = 8 ^ 17 = (7 + 1) ^ 17
We needn't expand this because the 18th ( the last term ) in this expansion will be 1 and the rest of the terms will have 7 as one of the factors. Hence the remainder would be 1.


to solve for the 3^19 question as well

3^19 = 3^3*3^16 = 3^3*9^8 = 3^3*81^4 = 3^3*(80+1)^4

like before the (80+1)^4 only has one term that isnt divisible by 10, namely 1.

so we get the remainder as 1*3^3 = 27, but 27 is greater than 10 so the remainder is 27/10 which is 7.
  [#permalink] 08 Sep 2006, 05:27
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic What is the remainder when you divide 2^200 by 7? carcass 7 02 Oct 2011, 10:50
What is integer n? 1. When divided by 7, remainder is 3 2. alimad 4 27 Sep 2006, 12:35
What is the remainder of 2 ^51 divided by 7 briozeal 7 01 Jul 2006, 09:26
What is integer n? 1. When divided by 7, remainder is 3 2. vivek123 13 02 Apr 2006, 09:55
What is the remainder when 7^345 +7^11 -2 is divided by 7 joemama142000 6 20 Feb 2006, 22:30
Display posts from previous: Sort by

What is the remainder of 2 ^51 divided by 7 ? What is the

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.