Remainders

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?

  1. 53
  2. 75
  3. 41
  4. 80

Answer

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.