Question

Kia recalls 5 digits of a 7-digit number and marks A and B in place of the remaining 2 digits.
654A27B

She later recalls that the number is exactly divisible by 24.
If A and B are the smallest numbers, then find the sum of A and B.

• A. 5
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

For a number to be divisible by 24, it should be divisible by 3 and 8.

For a number to be divisible by 8, the last three digits should be divisible by 8.
Last three digits = 27B
$$\begin{array}{c}3\\ 827B\\ -\underset{–}{24}\\ 3B\end{array}$$

For 3B to be exactly divisible by 8, 2 should come in place of B as we know that 32 is exactly divisible by 8.

Now, for a number to be divisible by 3, the sum of the digits of the number should be divisible by 3.

Sum of digits = 6 + 5 + 4 + A + 2 + 7 + 2 = 26 + A
Keeping the value of A as 1:
26 + 1 = 27

This is exactly divisible by 3.

Sum of A and B = 1 + 2 = 3