If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
OA: A
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
OA: A
1) x = 4n + 2, where n is a positive integer
if n=1, x=6. the given expression becomes 3^6+1
last digits of powers of 3 (3^1=3, 3^2=9, 3^3=7, 3^4=1, 3^5....) follow a cyclic pattern, repeats after every 4 terms. 3^6 has the same last digit as 3^2 ie 9.
9+1 divisible by 10
if n=3, x=14 the expression becomes 3^14+1. 3^14 has the same last digit as 3^2 ie 9. ((14/4 leaves remainder 2.)
9+1 divisible by 10
for any n, the given expression will be divisible by 10.
sufficient
2) x>4
say x=5
3^5+1. 3^5 has last digit 3. the last digit of the expression is 3+1=4 not divisible by 10
say x=6. 3^6+1 is divisible by 10 as shown above.
not sufficient
hence A
