Remainders

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

  1. 676
  2. 777
  3. 683
  4. 666

Answer

Two digit number is of the form: 7a+3 (a = 1 to 13)

The number forms Arithmetic Progression with common difference of 7. First term is 10. Last term is 94.

Number of Terms = 13

Sum = n(a+l)/2 = (13*104)/2 = 676

The correct option is A.