Question

a and b are two number when divided by 7 leaves a remainder 3 and 5. what will be the remainder when a-b is divided by 7 ? a. 4 b. 5 c. 6 d. 7

Answer 1

Dividend (number being divided) = Divisor x Quotient + Remainder

So, A = 7p + 3 and B = 7q + 5

Here p and q are the respective quotients (non-negative integer values).

Clearly, A - B = 7p + 3 - 7q - 5 = 7(p - q) - 2

Now on using the basic identity of a division, this equation implies that when (A - B) is divided by 7, the quotient is (p - q) and the remainder is -2.