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If the square of a two-digit number is reduced by the square of the number formed by reversing the digits of the number, the final result is:
  • a)
    Divisible by 11
  • b)
    Divisible by 9
  • c)
    Divisible by both 9 and 11
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the square of a two-digit number is reduced by the square of the n...
Given
Let the two-digit number be (10x + y)
According to the question,
⇒ (10x + y)2 - (10y + x)2
⇒ 100x2 + y2 + 20xy - 100y2 - x2 - 20xy
⇒ 99x2 - 99y2 = 99(x2 - y.)
As 99 is divisible by both 9 and 11
So, the result is also divisible by 9 and 11
∴ The correct answer is both 9 and 11
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If the square of a two-digit number is reduced by the square of the number formed by reversing the digits of the number, the final result is:a)Divisible by 11b)Divisible by 9c)Divisible by both 9 and 11d)None of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
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