2023 · Q82
How many three-digit numbers are possible such that the difference between the original number and the number obtained by reversing the digits is 396? (no digit is repeated)
general-mental-abilityquantitative-aptitude
- A4
- B5
- C50
- D40
Explanation
For a three-digit number 100a+10b+c, subtracting its reversal gives 99(a-c) = 396, so a-c = 4. Since the reversed number must also be three-digit, c cannot be zero, giving a in {5, 6, 7, 8, 9}, five choices. The middle digit b can then be any of the remaining 8 digits, with no repetition. The total count is 5 x 8 = 40 numbers. Hence option D.