Question : If the sum of the digits of any integer lying between 100 and 1000 is subtracted from the number, the result is always divisible by:
Option 1: 6
Option 2: 2
Option 3: 9
Option 4: 5
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Correct Answer: 9
Solution :
Let the three-digit number be ABC.
So, ABC = 100A + 10B + C
The sum of the digits ABC = A + B + C
Therefore, (100A + 10B + C) – (A + B + C) = 99A + 9B
= 9(11A + B)
So, when (A + B + C) is subtracted from that integer, the result is always divisible by 9.
Hence, the answer is 9.
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