Question

If the difference between a 3-digit number abc and the number obtained by reversing its digits is divided by 11, the quotient obtained is always a multiple of ___.

• A. 9
• B. a + b
• C. 11
• D. a + c

Answer 1

The correct option is A 9

General form of the 3-digit number abc is 100a + 10b + c

By reversing the digits, we get the number cba.

Now, general form of the 3-digit number cba is 100c + 10b + a

The difference
= (100a + 10b + c) - (100c + 10b + a)
= 100a + 10b + c - 100c - 10b - a
= 99 (a - c)
If we divide it by 11,
the quotient is 9(a - c)
So, the quotient is a multiple of 9.