Question

How many 4-digit numbers of the form AB61 are there that are divisible by 11 (where A and B are distinct digits)?

• A. 3
• B. 4
• C. 7
• D. 13
• E. 14

Answer 1

Answer: (B)

4

Answer 2

Divisibility rule of 11 says that the difference of the alternative sum of the digits should be a multiple of 11.
Therefore, the number AB61 will be a divisible by 11 if $(A – B + 6 – 1)$ is multiple of 11.
That is, $A – B + 6 – 1 = 11k$
$⇒ A – B = 11k – 5 ⇒ A – B = –5$
Therefore, possible pairs of A and B are (1, 6), (2, 7), (3, 8) and (4, 9).
Hence, 4 such four-digit numbers are possible.
The correct answer is B

The Correct Option is (B):2 and 3 only