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Question

Let n N, n>25. Let A, G, H denote the arithmetic mean. Geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H {25, 26,...... n} is


A

49

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B

81

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C

169

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D

225

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Solution

The correct option is D

225


A=25+n2,G=5n, H=50n25+n

As A, G, H are natural numbers, n must be odd pefect square. Now H will be a natural number, if n=225.(verify from options)


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