Question : If the sum of digits of any number between 100 and 1000 is subtracted by the same number, the resulting number is always divisible by:
Option 1: 2
Option 2: 5
Option 3: 6
Option 4: 9
Correct Answer: 9
Solution :
Let's consider a number with three digits, a, b, and c.
The value of this number can be expressed as follows: 100a + 10b + c
Subtracting the sum of the digits from the number,
(100a + 10b + c) – (a + b + c) = 99a + 9b = 9 (11a + b)
Hence, the resulting number is always divisible by 9.
Option 4 is correct.
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