If the number 583p2310q2 is divisible by 11 then, what is the value of p x q, where p > q?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 0.
To be divisible by 11, the difference between the sum of digits at even & odd places must either be 0 or equal to 11 for a number
⇒ (5 + 3 + 2 + 1 + q) = (8 + p + 3 + 0 + 2)
⇒ (11 + q) = (13 + p)
⇒ q - p = 2 ( not possible, p > q given)
Condition (1)
⇒ 13 + p - (11 + q) = 11
⇒ 13 + p - 11 - q = 11
⇒ p - q + 2 = 11
⇒ p - q = 9
This condition is only possible only if we put p = 9 and q = 0, as we can put only single-digit numbers
Hence,
⇒ p × q = 9 × 0 = 0