If the number 6523678pq is divisible by 99, the missing digits p and q are:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. p = 2, q = 6.
Concept used:
Divisibility rule of 9: if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9
Divisibility rule of 11: If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
Calculations:
For a number to be divisible by 99, it should be divisible by 9 and 11
For 9: 6 + 5 + 2 + 3 + 6 + 7 + 8 + p + q is divisible by 9
⇒ 37 + p + q is divisible by 9 (45 is the nearest multiple of 9 to the sum)
⇒ p + q = 8
For 11: (6 + 2 + 6 + 8 + q) - (5 + 3 + 7 + p) = 11
⇒ 22 + q - 15 - p = 11
⇒ q - p = 4
Solving equation 1 and 2 we get
q = 6 and p = 2