A number is divisible by 24 means a number is divisible by both 3 and 8 individually.
11p9q4 is divisible by 8 means last three digits (9q4) must be divisible by 8.
Possible values of q = 0, 4, 8 [We cannot take 0 as a value of 'q' because it will make the product 0 and we will never get the maximum possible value.]
When q = 4:
Sum of digits of number = 1 + 1 + p + 9 + 4 + 4 = 19 + p
Possible values of p = 2, 5, 8
Possible values of 'pq' = 8, 20, 32
When q = 8:
Sum of digits of number = 1 + 1 + p + 9 + 8 + 4 = 23 + p
Possible values of p = 1, 4, 7
Possible values of 'pq' = 8, 32, 56
So, maximum possible value of 'pq' = 56
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