DS Question - 10

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ?

(1) n- 2 is divisible by 5.

(2) t is divisible by 3.

Answer - C

Statement (1) alone - no sufficient information about t
Statement (2)alone - no sufficient information about n

From the ques --- n = a*3 + 2

t = b*5 + 3

Using Statement (1) --- n = p*5 + 2

Thus n = 15*k + 2

Using Statement (2) --- t = q*3 + 3

Thus t = 15*j + 3

nt = 15*k(15*j + 3) + 30*j + 6

=> always leaves a remainder of 6 when divided by 15.