Multiple choice

A number x, when divided by d, leaves a remainder 10. Another number y, when divided by the same divisor, leaves 11 as remainder. If (x + y), when divided by 'd', leaves 5 as remainder, find the value of d.

  1. 16

  2. 14

  3. 12

  4. 10

  5. None of these
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A Correct answer
Explanation

x = q1*d + 10; y = q2*d + 11. x+y = (q1+q2)*d + 21. Dividing by d leaves remainder 5. 21 = k*d + 5. 16 = k*d. Since the remainder must be less than the divisor, d > 11. The only factor of 16 greater than 11 is 16.

AI explanation

Using the basic remainder theorem, the remainder of a sum is the sum of the individual remainders. Thus, (x + y) gives an initial remainder of 10 + 11, which equals 21. Since dividing 21 by d leaves a remainder of 5, the divisor d must be 21 - 5, so d is 16.

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