Which of the following pairs of non-zero values of p and q make 6-digit number 674pq0 divisible by both 3 and 11?

Solution (By Examveda Team)

Given:
674pq0 is divisible by both 3 and 11
Concept used:
If the sum of digits of a number is a multiple of 3, the number will be completely divisible by 3
If the difference of the sum of alternative digits of a number is 0 or divisible by 11, then that number is divisible by 11 completely.
Calculation:
As 674pq0 divisible by 3
So, 6 + 7 + 4 + p + q + 0
⇒ 17 + p + q also divisible by 3
Now,
Possible values of p + q = 4, 7, 10, 13, 16
From the options
Option A and Option D is satisfying
Now,
For Option A
The number is 674220
So, 6 + 4 + 2 - 7 - 2 = 3 Not divisible by 11
For Option D
The number is 674520
So, 6 + 4 + 2 - 7 - 5 = 0 divisible by 11
∴ The required answer is Option D.