Question

The number of integers of the form 3AB4, where A, B denote some digits, which are divisible by 11 is

A. 0

B. 4

C. 7

D. 9

Answer 1

The number is of the form 3AB4.

Here, 3 − A + B − 4 = B − A − 1

3AB4 is divisible by 11 if B − A − 1 is divisible by 11.

B − A − 1 is divisible by 11.

⇒ B − A − 1 = 0 or 11

⇒ B − A = 1 or 10

However, B − A cannot be equal to 10 as A and B are digits.

∴ B − A must be 1.

Therefore, the possible values of A and B are (1, 0), (2, 1), (3, 2), (4, 3), (5, 4), (6, 5),

(7, 6), (8, 7) and (9, 8)

Hence, the correct answer is D.