Multiple choice

A number when divided by a divisor leaves a remainder of 37. When twice the original number is divided by the same divisor, the remainder is 19. What is the value of the divisor?

  1. 53

  2. 54

  3. 55

  4. 56
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C Correct answer
Explanation

When N divided by d leaves remainder 37, N = qd + 37. When 2N is divided by d, remainder is 19, so 2N = 2qd + 74. The remainder when 74 is divided by d is 19, meaning 74 = kd + 19, so d divides (74-19) = 55. Since remainder 37 requires d > 37, and divisors of 55 are 1, 5, 11, 55, only d = 55 satisfies d > 37.

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