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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)Necessarily irrational
- d)(A) & (B) both
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the square of a two digit number is reduced by the square of the nu...
Let the number be XY→ (10X + Y)2 – (10Y – X)2
= 99 X2 – 99Y2 (which is divisible by both 9 & 11).
= 99 X2 – 99Y2 (which is divisible by both 9 & 11).
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If the square of a two digit number is reduced by the square of the nu...
Let the two-digit number be $10a+b$. The square of this number is $(10a+b)^2 = 100a^2 + 20ab + b^2$. The number formed by reversing the digits is $10b+a$. The square of this number is $(10b+a)^2 = 100b^2 + 20ab + a^2$. Subtracting these two expressions, we get \[100a^2 + 20ab + b^2 - (100b^2 + 20ab + a^2) = 99a^2 - 99b^2 = 99(a^2-b^2) = 99(a-b)(a+b).\]Since $a$ and $b$ are digits, $a-b$ is an integer between $-9$ and $9$, inclusive. Hence, $a-b$ is a factor of $99(a-b)(a+b)$. Therefore, the expression is divisible by $\boxed{9}$.
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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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer?
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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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer?.
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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Necessarily irrational d)(A) & (B) bothCorrect answer is option 'D'. Can you explain this answer?.
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