If the number 6p5157q is divisible by 88, then p × q = ______, where p and q are single digit numbers.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18.
Divisibility by 8: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Divisibility by 11: A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11.
The last three digits of the number = 57q
For this to be divisible by 8, q must be 6 (since 576 is divisible by 8)
Sum of digits at odd places = 6 + 5 + 5 + q = 16 + q = 16 + 6 = 22
Sum of digits at even places = p + 1 + 7 = 8 + p
Difference: (22) - (8 + p) = 14 - p
For divisibility by 11, (14 - p) must be either 0 or divisible by 11
If p = 3, then 14 - 3 = 11
Also, 22 - 11 = 11
Then, p = 3 and q = 6
So, p × q = 3 × 6 = 18
Therefore, the required value is 18.