Civil Services Examination · Question 66
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A - B is a multiple of 27, where A > B, how many such different A's are possible?
Show answer & explanation
Answer: (B) 9
Explanation
A - B = 9(a - b), so a - b must be a multiple of 3. With b ≥ 1 (B is 2-digit): a - b = 3 gives 6 numbers (41 to 96), a - b = 6 gives 3 (71, 82, 93). Total 9.