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KVPY2011MathematicsSequences and Series

The arithmetic mean and the geometric mean of two distinct 2 -digit numbers x and y are two integers one of which can be obtained by reversing the digits of the other (in base 10 representation). Then x+y equals-

Options

  1. A82
  2. B116
  3. C130
  4. D148

Correct answer

C. 130

Step-by-step solution

x+y 2 =10 a+b, x y =10 b+a (a, b N)x y=(10 b+a)²(x-y)²=4(11 a+11 b)(9 a-9 b)=4 11 (a+b) 9(a-b) a+b=11, a-b=1a=6, b=5 ((x-y)² . is perfect square of an integer) x+y=130

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