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Q: A number when divided by 280 leaves 73 as the remainder. When the same number is divided by 35, the remainder will be:
  • A. 4
  • B. 2
  • C. 3
  • D. 7
Correct Answer: Option C - Let number = N N = 280K + 73 = (358) K + 70 + 3 = 35 (8K + 2) + 3 N = 35m + 3.....(i) (where, m = 8 K + 2) or N = 35q + r ......(ii) On comparing both equation, r = 3 Hence, on dividing the same numbers by 35 the remainder will be 3.
C. Let number = N N = 280K + 73 = (358) K + 70 + 3 = 35 (8K + 2) + 3 N = 35m + 3.....(i) (where, m = 8 K + 2) or N = 35q + r ......(ii) On comparing both equation, r = 3 Hence, on dividing the same numbers by 35 the remainder will be 3.

Explanations:

Let number = N N = 280K + 73 = (358) K + 70 + 3 = 35 (8K + 2) + 3 N = 35m + 3.....(i) (where, m = 8 K + 2) or N = 35q + r ......(ii) On comparing both equation, r = 3 Hence, on dividing the same numbers by 35 the remainder will be 3.