remainders

[prithviforever]

when positive integer n is divided by 3, the remainder is 2; and when a positive integer t is divided by 5, the remainder is 3. what is the remainder when product n*t is divided by 15?
(1)n-2 is divisible by 5
(2)t is divisible by 3

[Frankenstein]

n=3a+2, t=5b+3
from(1): n-2 is divisible by 5, that means (n-2)=3a is divisible by 5 so a is of the form 5.p, where p is an integer.
so n = 15p+2 and n.t= (15p+2)(5b+3) = 15p(5b+3) + 2(5b+3) when divided by 15 is the remainder when (10b+6) is divided by 15. So, the remainder is either 1 or 6 or 11.
Insufficient

from(2): t=5b+3 is divisible by 3 so b must be a multiple of 3. Hence, t = 5.(3q)+3 = 15q+3
So, n.t = (3a+2)(15q+3) = 15q(3a+2) + (3a+2).3 when divided by 15 is the remainder when (9a+6) is divided by 15. So, the remainder is either 0,3,6,9or12
Insufficient

Using, both (1)&(2), we get the remainder as 6.
Sufficient

Hence, C