Question : If the sum of the digits of a three-digit number is subtracted from that number, then it will always be divisible by:
Option 1: 3 only
Option 2: 9 only
Option 3: Both 3 and 9
Option 4: 3, 6, 9
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Correct Answer: Both 3 and 9
Solution :
Let abc be the three-digit number.
abc = 100a + 10b + c (here a, b, and c are digits)
According to the question,
If we subtract (a + b + c) from (100a + 10b + c)
= 100a + 10b + c – (a + b + c)
= 100a + 10b + c – a – b – c
= 99a + 9b
= 9(11a + b)
Here we can see that 9 is a common factor.
Thus the resulting difference is always divisible by 9. And we know that a number that is divisible by 9 is also divisible by 3.
Hence, the correct answer is both 3 and 9.
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