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

 It is currently 24 Apr 2015, 16:27

### 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 reminder of 7^381 divided by 5

Author Message
TAGS:
Senior Manager
Joined: 02 Oct 2005
Posts: 303
Followers: 1

Kudos [?]: 7 [0], given: 0

What is the reminder of 7^381 divided by 5 [#permalink]  10 Oct 2005, 20:16
What is the reminder of 7^381 divided by 5
Manager
Joined: 15 Jul 2005
Posts: 106
Followers: 1

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

The remainder is 2. We only need to know the last digit of 7^381 to know the remainder.

last digits are
7^0=1
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7

as you may notice, the last digits repeat every 4 powers, ie., last digit of 7^2 = last digit of 7^6, etc.

381 is one more than 380 (which is divisible by 4), thus 7^381 will have the last digit 7, therefore the remainder will be 2
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 5

Kudos [?]: 37 [0], given: 0

chets wrote:
The remainder is 2. We only need to know the last digit of 7^381 to know the remainder. last digits are
7^0=1
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7
as you may notice, the last digits repeat every 4 powers, ie., last digit of 7^2 = last digit of 7^6, etc.

381 is one more than 380 (which is divisible by 4), thus 7^381 will have the last digit 7, therefore the remainder will be 2

this is the best approach. first find the pattren, then AC.
Director
Joined: 21 Aug 2005
Posts: 793
Followers: 2

Kudos [?]: 9 [0], given: 0

There has to be a pattern here. Let's see -
7^1 = 7 (rem - 2 when div by 5)
7^2 = 49 (rem - 4)
7^3 = 343 (rem - 3)
7^4 = 2401 (rem - 1)
7^5 = 16807 (rem - 2)
7^6 = 117649 (rem - 4)
...
I would stop here and believe that there is a pattern in the remainder, else I'll be doing this problem for whole duration of the test (and may still not complete it in the end! )

7^381 = 7^(4(95) + 1)
so this is the 5 th in the sequence pattern and hence has the remainder as 2
Am I correct! Please say yes!
Senior Manager
Joined: 02 Oct 2005
Posts: 303
Followers: 1

Kudos [?]: 7 [0], given: 0

gsr your answer is correct. But Chets approach is more preferred. Reason, it involves less calculation; hence less prone to error and saves time.

Hope you agree with me.
Director
Joined: 21 Aug 2005
Posts: 793
Followers: 2

Kudos [?]: 9 [0], given: 0

sudhagar, It's true. I agree. But both methods are same and to make it more explainatory (one won't this liberty in the exam!), i listed out all the digits
Similar topics Replies Last post
Similar
Topics:
1 give n is a positive integer, what is the reminder when 3^n is divided 3 01 Feb 2015, 14:42
31 What is the remainder when 43^86 is divided by 5? 28 21 Jun 2012, 15:59
What is the reminder when the positive integer x is divided 1 25 Apr 2011, 08:22
What is the reminder when the positive integer n is divided 12 13 Oct 2008, 09:06
DS: What is the reminder 1 24 Jun 2006, 20:25
Display posts from previous: Sort by