After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?
Let the number be N. First, N is divided by 3 and then the quotient obtained is divided by 4.
You are required to calculate from back-end.
Number when divided by 7 gives remainder 4 = (7k+4)
Required Number, N = 3[4(7k+4)+1]+2 (Successive Division)
N = 84k + 53
When N is divided by 84, remainder is 53.
The correct option is A.