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The difference of the squares of two distinct two-digit numbers with one being obtained by reversing the digits of the other is always divisible by
Question

The difference of the squares of two distinct two-digit numbers with one being obtained by reversing the digits of the other is always divisible by

A.

4

B.

6

C.

10

D.

11

Correct option is D

Given:

  • Two numbers: 10a + b and 10b + a, where a and b are the digits.

Formula:
Difference of squares = (10a + b)2 - (10b + a)2.

Solution:


  1. 22
    Expand: (10a + b) - (10b + a) = [(10a + b) + (10b + a)] × [(10a + b) - (10b + a)] = (11a + 11b) × (9a - 9b)

  2. Factor out common terms: = 11 × 9 × (a + b) × (a - b)
  3. Clearly, the result is always divisible by 11.

Final Answer: (d) 11

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