I took long time for this so I hope there is a short-cut.
Together,
Stmt 1: n=3i+2=5j+2
By trial and error, remainder of n by 15 would be 2. Donno about t, so insuff.
Stmt 2: t=5p+3=3q
by trying small values for p, remainder of t by 15 is 3. Donno about n so insuff.
Together,
n=15a+2
t=15b+3
So multiplying, remainder of nt by 15 has to be 6.