Problem Solving

The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

(1) n - 2 is divisible by 5
(2) t is divisible by 3

Answer : C - Explanation to follow !

Note: Oops typo! Edited now

n=Qx3+2 Q>=0, n={2,5,8,11,14,17,20,23,26,29,32,...}, n=2+(N-1)3
t=Zx5+3 Z>=0, z={3,8,13,18,23,28,33,...}, t=3+(N-1)5

1.)n-2 is divisible by 5
- n={2,17,32,47,62,...}, n=2+(N-1)15
- we do not know anynothing NEW about t
- so let try to multiply few options from n and t

17x3=51 => 51/15=3x15+6, remainder is 6
17x8=136 => 136/15=9x15+1, remainder is 1

INSUFFICIENT

2.)t is divisible by 3
- t={3,18,33,48,...}, t=3+(N-1)15
- we do not know anything NEW about n
- so let try to multiply few options from n and t

2x3=6 => 6/15=0x15+6
3*18=54 => 54/15=3x15+9

INSUFFICIENT

1+2)
- n={2,17,32,47,62,...}
- t={3,18,33,48,...}
- so let try to multiply few options from n and t

17*3=51 => 51/15=3x15+6
17*33=561 => 561/15=37*15+6

C - SUFFICIENT

rnaah wrote:The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

(1) n - 2 is divisible by 5
(2) t is divisible by 3

should be C
based on given info...

n = 3p + 2, t = 5k + 3
so remainder to be found when nt/15

1) n-2 = 5q
n=5q+2
but from given data, when combined with above
n = 15q + 2
still we cannot say anything about the remainder when nt = (15q + 2)(5k+3) is divided by 15 because 5k+3 term in the product might give 2 or 5 or 8

2) t = 3m
but from given data, when combined with above
t = 15m + 3
still we cannot say anything about the remainder when nt = (3p + 2)(15m + 3) is divided by 15 because first term in the product gives 3 or 8 or 13

combining above two...
then nt = (15q + 2)(15m + 3), which is clearly divisble by 15 with remainder 2*3 = 6

hence C
while solving you can eliminate 10% of the steps by doing most steps mentally

rnaah wrote:The remainder when n is divided by 3 is 2 and the remainder when t is divided by 5 is 3. What is the remainder when nt is divided by 15?

(1) n - 2 is divisible by 5
(2) t is divisible by 3

I posted a solution here:

https://www.beatthegmat.com/remainders-t ... cityevent=

IMO: C