Author 
Message 
Director
Joined: 01 Apr 2008
Posts: 872
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

PS: remainder [#permalink]
Show Tags
24 Mar 2009, 22:44
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 0 sessions
HideShow timer Statistics
This topic is locked. If you want to discuss this question please repost it in the respective forum.
This topic is locked. If you want to discuss this question please repost it in the respective forum.
If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5? A. 0 B. 1 C. 2 D. 3 E. 4
Note: It is 3 raised to the power (8n+3).



Manager
Joined: 02 Mar 2009
Posts: 134

Re: PS: remainder [#permalink]
Show Tags
25 Mar 2009, 00:06
The answer is E..
Good explanations are provided below.
Last edited by shkusira on 26 Apr 2009, 07:01, edited 1 time in total.



Intern
Joined: 05 Nov 2008
Posts: 1

Re: PS: remainder [#permalink]
Show Tags
25 Mar 2009, 02:07
I think Answer is E.
We look at the last digit for case divide by 5
3^(8n+3) + 2 = ((3^8)^n * 3^3) + 2 = ((6561)^n * 27) + 2 = ...7 + 2 = ...9
ps. (6561)^n < the last digit is always 1.
from above the last digit is 9 so 9/5 has the remainder = 4.
Last edited by Takumi on 25 Mar 2009, 02:18, edited 1 time in total.



Intern
Joined: 05 Dec 2008
Posts: 18

Re: PS: remainder [#permalink]
Show Tags
25 Mar 2009, 02:16
Agree with E.
if n=1 unit digit of 3 ^(8+3) is 7 unit digit of 3^11 + 2 is 9 when unit digit 9 divided by 5, the remainder is 4
consider whatever n is positive integer , unit digit of 3^(8n+3) is 7
then the answer is E.



Manager
Joined: 22 Feb 2009
Posts: 65

Re: PS: remainder [#permalink]
Show Tags
25 Mar 2009, 02:36
Last digit of 3^n will be 3,9,7,1 ( 3^1,3^2,3^3,3^4) and this cycle will repeat.
3^(8n+3) + 2 = ((3^8)^n * 3^3) + 2
(3^8) last digit will be 1 hence for (3^8)^n, last digit will be 1
Last digit for 3^3 is 7. Last digit for expression 3^(8n+3) will be 7
Hence last digit for 3^(8n+3) + 2 will be 9. If divided by 5 remainer will be 5.
irrespective of a digit at 10th place for this equation.
Cheers,



Manager
Joined: 28 Jul 2004
Posts: 135
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth

Re: PS: remainder [#permalink]
Show Tags
25 Mar 2009, 13:27
Unit digit of 3^8n = 1 Unit digit of 3^3 = 7 So, unit digit of 3^8n x 3^3 = 7 > unit digit +2 = 9 > remainder is 4 when divided by 5 > answer is E
_________________
kris



Director
Joined: 25 Oct 2008
Posts: 591
Location: Kolkata,India

Re: PS: remainder [#permalink]
Show Tags
02 Jul 2009, 03:36
Ah!The great cycle theory!Wonderful.
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902










