Question

Jenna is recalling Andrew's mobile number. The starting 3-digit number is the area code 972.

She recalls that two digits out of the next three digits is 38, and the next two digits of the three digits is 67. So, the number is:
972-38X-67Y

If the mobile number is exactly divisible by 24, find the sum of X and Y.
(Use the smallest values of X and Y.)

• A. 3
• B. 2
• C. 5
• D. 6

Answer 1

The correct option is A 3

We know, $24=8\times 3$
So, the number has to be divisible by 8 and 3.

For a number to be divisible by 8, the last three digits must be divisible by 8.
67Y
$$\begin{array}{c}8\\ 867Y\\ -\underset{–}{64}\\ 3Y\end{array}$$

For 3Y to be exactly divisible by 8, the number 2 should come in place of Y, 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 a number should be divisible by 3.

Sum of digits = 9 + 7 + 2 + 3 + 8 + X + 6 + 7 + 2 = 44 + X

Keeping the value of X as 1, we get
44 + 1 = 45

Therefore, Andrew's mobile number is:
972-381-672.

Sum of X and Y = 1 + 2 = 3