The difference between a three-digit number (with non-repeating digits) and the same number in the reverse order is always divisible by

Correct option is A

Given:

• A three-digit number can be expressed as $100x+10y+z$, where $x$, $y$, and $z$ are its digits.
• Its reverse can be expressed as $100z+10y+x$.
• We need to find what the difference between the number and its reverse is always divisible by.

Formula and Concept:

1. The difference between the original number and its reverse is:
   (100x + 10y + z) - (100z + 10y + x).
2. Simplify the difference to factorize and determine its divisibility.

Solution:

1. Start with the difference:
   (100x + 10y + z) - (100z + 10y + x).
   Simplify:
   100x - x + 10y - 10y + z - 100z = 99x - 99z.

2. Factorize:
   99(x - z).

3. The difference is always a multiple of 99.
   The factors of 99 are 3, 11, and 33.

4. Therefore, the difference is always divisible by 33.

Final Answer:

(a) 33.