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

 It is currently 06 May 2015, 12:12

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

Author Message
TAGS:
SVP
Joined: 05 Jul 2006
Posts: 1519
Followers: 5

Kudos [?]: 115 [0], given: 39

What is the remainder of 2 ^51 divided by 7 ? What is the [#permalink]  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
Joined: 11 May 2006
Posts: 260
Followers: 1

Kudos [?]: 6 [0], given: 0

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
Joined: 11 May 2006
Posts: 260
Followers: 1

Kudos [?]: 6 [0], given: 0

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
Joined: 30 Jun 2006
Posts: 87
Followers: 0

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

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
Joined: 05 Jul 2006
Posts: 1519
Followers: 5

Kudos [?]: 115 [0], given: 39

jainvik7

Very comprehensive approach... very
Manager
Joined: 30 Jun 2006
Posts: 87
Followers: 0

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

Thanks,
iced_tea and yezz
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

IMO second Q can be re-phrased as; What is the last digit of 3^19 ? It is 7 .
Current Student
Joined: 29 Jan 2005
Posts: 5244
Followers: 23

Kudos [?]: 179 [0], given: 0

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
Joined: 04 May 2006
Posts: 40
Followers: 0

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

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.
Similar topics Replies Last post
Similar
Topics:
4 What is the remainder when you divide 2^200 by 7? 7 02 Oct 2011, 10:50
What is the remainder when 7^n + 2 is divided by 5 (1) when 2 19 Jun 2008, 03:51
What is the remainder of 2 ^51 divided by 7 7 01 Jul 2006, 09:26
What is integer n? 1. When divided by 7, remainder is 3 2. 13 02 Apr 2006, 09:55
What is the remainder when 7^345 +7^11 -2 is divided by 7 6 20 Feb 2006, 22:30
Display posts from previous: Sort by