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Select the correct answerTwo different numbers when divided by a divisor left reminder 11 and 21 respectively. When their sum was divided by the same divisor reminder was 4. what is the divisor?Options15835928

Question

Select the correct answerTwo different numbers when divided by a divisor left reminder 11 and 21 respectively. When their sum was divided by the same divisor reminder was 4. what is the divisor?Options15835928

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Solution

Let's denote the two different numbers as A and B, and the divisor as D.

From the problem, we know that:

A = D*q1 + 11 (where q1 is some quotient)

B = D*q2 + 21 (where q2 is some quotient)

Adding these two equations, we get:

A + B = D*(q1 + q2) + 32

But we also know from the problem that when A + B is divided by D, the remainder is 4. So we can write:

A + B = D*q3 + 4 (where q3 is some quotient)

Comparing these two equations, we can see that:

D*(q1 + q2) + 32 = D*q3 + 4

This simplifies to:

D*(q1 + q2 - q3) = 4 - 32 = -28

Since D must be a positive integer, the only possible value from the options given that can satisfy this equation is D = 28.

This problem has been solved

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