Question:
How many 4-digit numbers of the form AB61 are there that are divisible by 11 (where A and B are distinct digits)?
How many 4-digit numbers of the form AB61 are there that are divisible by 11 (where A and B are distinct digits)?
Updated On: Oct 11, 2024
- 3
- 4
- 7
- 13
- 14
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The Correct Option is B
Solution and Explanation
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
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
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