Question

If the sum of the digits of any number lying between 100 and 1000 is subtracted from the number, the difference is always divisible by
1. 9
2. 12
3. 6
4. None of the above

Answer 1

Correct Answer - Option 1 : 9

Calculation

Numbers lying between 100 and 1000 will be three-digit numbers

Let the number be xyz

⇒ xyz = 100x + 10y + z

The sum of the digits = x + y + z

Subtracting the sum of the digits from the number we get,

(100x + 10y + z) - (x + y + z) = 99x + 9y

⇒ 9(11x + y) which is always divisible by 9