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Question

The difference beween a 3-digit number ABC and the number obtained by interchanging it's digits is always divisible by:
  1. 4
  2. 7
  3. 99
  4. 22


Solution

The correct option is C 99

The 3-digit number ABC can be written as 100A + 10B + C

Similarly CBA can be written as: 
100C + 10B + A

Difference
= (100A + 10B + C) - (100C + 10B + A)
= 100A + 10B + C - 100C - 10B - A
= 99 (A - C)

=9×11(AC)=3×3×11(AC)

This number is divisible by only 3 ,9, 11 and 99. 

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