When a certain positive integer P is divided by another positive integer, the remainder is r_1 . When a second positive integer Q is divided by the same integer, the remainder is r_2 and when (P + Q) is divided by the same divisor, the remainder is r_3 . Then the divisor may be :

Answer: Option D

Let P = x + $$r_1$$ and Q = y + $$r_2$$, where each of x and y are divisible by the common divisor.
Then, P + Q = (x + $$r_1$$) + (y + $$r_2$$)
                    = (x + y) + ($$r_1$$ + $$r_2$$)
(P + Q) leaves remainder $$r_3$$ when divided by the common divisor.
⇒ [(x + y) + ($$r_1$$ + $$r_2$$) - $$r_3$$] is divisible by the common divisor.
Since (x + y) is divisible by the common divisor, so divisor = $$r_1$$ + $$r_2$$ - $$r_3$$