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
Can anyone help pls?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
1-12
This topic has expert replies
-
Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
dunkin looks like you are struggling with Number Systems
3^8n+(3 + 2)
when divided by we will be left with 3^8n only
I can write 3^8n as (3^2)^4n = 9^4n
When 9 is divided by 5 remainder is -1 but -1 raised to Even Power = +1
Hence remainder will be +1
3^8n+(3 + 2)
when divided by we will be left with 3^8n only
I can write 3^8n as (3^2)^4n = 9^4n
When 9 is divided by 5 remainder is -1 but -1 raised to Even Power = +1
Hence remainder will be +1
-
jayhawk2001
- Community Manager
- Posts: 789
- Joined: Sun Jan 28, 2007 3:51 pm
- Location: Silicon valley, California
- Thanked: 30 times
- Followed by:1 members
3^8n*3^3 + 2dunkin77 wrote: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
Can anyone help pls?
3^8 = 9^4 will have 1 as the units digit. So, 3^8n*3^3 will have 7 as the
units digit.
7 + 2 = 9, when divided by 5 will give 4 as the remainder.
I wasn't too clear on whether the question is 3^(8n+3) + 2 or
3^8n + (3 + 2)
-
Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
Did I misread the question??
Is it 3^(8n+3) +2 ??
3^(8n+3) = (3^8n).3^3
3^8n = (3^2)^4n = 9^4n. Now 9 when divided by 5 leaves remainder -1 but this -1 is raised to an even power so you get +1 and are left with 3^3
Now 3^3 +2 = 29 which when divided by 5 leaves remainder 4
Is it 3^(8n+3) +2 ??
3^(8n+3) = (3^8n).3^3
3^8n = (3^2)^4n = 9^4n. Now 9 when divided by 5 leaves remainder -1 but this -1 is raised to an even power so you get +1 and are left with 3^3
Now 3^3 +2 = 29 which when divided by 5 leaves remainder 4
