A six-digit number 11p9q4 is divisible by 24. Then the greatest possible value for pq is:

Correct option is A

Given:

A six-digit number is represented as 11p9q4.

The number is divisible by 24.

Concept and Formula Used:

Divisibility by 24:

A number is divisible by 24 if it is divisible by both 8 and 3 (since 24=8×3).

Divisibility by 8: The last three digits of the number must be divisible by 8.

Divisibility by 3: The sum of all the digits of the number must be divisible by 3.

Solution:

As per the question;

If a number is divisible by 24, then it is also divisible by 8 and 3.

And if a number is divisible by 8, then its last 3 digits is also divisible by 8.

= 9q4 is divisible by 8.

Possible values of q = 0, 4, 8

If a number is divisible by 3, then sum of the no. is also divisible by 3.

(15 + p + q) is divisible by 3.

If we take q = 4, then p = 8, so pq = 32

And if we take q = 8 then p = 7, so pq = 56