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Q: When a number is divided by a divisor, the remainder is 16. When twice the original number is divided by the same divisor, the remainder is 3. Find the value of that divisor
  • A. 29
  • B. 51
  • C. 23
  • D. 53
Correct Answer: Option A - Let, the original number be N, the divisor be d, quotient be q. N = dq + 16 ∴ 2 N = 2(dq + 16) 2 N = 2dq + 32 When (2dq + 32) is divided d then remainder is 3. 2dq is completely divisible by d, then ∴ Required number = 32 – 3 = 29
A. Let, the original number be N, the divisor be d, quotient be q. N = dq + 16 ∴ 2 N = 2(dq + 16) 2 N = 2dq + 32 When (2dq + 32) is divided d then remainder is 3. 2dq is completely divisible by d, then ∴ Required number = 32 – 3 = 29

Explanations:

Let, the original number be N, the divisor be d, quotient be q. N = dq + 16 ∴ 2 N = 2(dq + 16) 2 N = 2dq + 32 When (2dq + 32) is divided d then remainder is 3. 2dq is completely divisible by d, then ∴ Required number = 32 – 3 = 29