Multiple choice

A and B are natural numbers which when divided by a divisor d leave remainders of 23 and 13 respectively. When A+B is divided by d, the remainder is 3. What is the value of d?

  1. 10

  2. 33

  3. 36

  4. 39
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B Correct answer
Explanation

A = q1*d + 23, B = q2*d + 13. A+B = (q1+q2)d + 36. Given A+B = q3*d + 3, so 36 = q4*d + 3, which means q4*d = 33. The divisor d must be a factor of 33 and greater than the remainders (23 and 13). The only factor of 33 greater than 23 is 33.

AI explanation

If A and B leave remainders of 23 and 13, their sum A + B leaves an initial remainder equal to the sum of those remainders, which is 23 + 13 = 36. When A + B is divided by d, the final remainder is 3, which means d perfectly divides 36 minus 3, or 33. Since a divisor must always be greater than the individual remainders it produces, d must be greater than 23, making the only possible value 33.

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