If (10 + _ 10 x), (10 + _ 10 y) and (10 + _ 10 z) are in AP, then consider the following statements: I. The GM of x and z is y^2. II. The AM of _ 10 x and _ 10 z is _ 10 y. Which of the statements given above is/are correct?

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Correct answer: B. II only

Given (10 + _ 10 x), (10 + _ 10 y), and (10 + _ 10 z) are in AP. 2(10 + _ 10 y) = (10 + _ 10 x) + (10 + _ 10 z) 20 + 2 _ 10 y = 20 + _ 10 x + _ 10 z 2 _ 10 y = _ 10 x + _ 10 z _ 10 y = _ 10 x + _ 10 z 2 This shows that the AM of _ 10 x and _ 10 z is _ 10 y. Thus, Statement II is correct. From 2 _ 10 y = _ 10 x + _ 10 z, we get: _ 10 y^2 = _ 10 (xz) y^2 = xz The GM of x and z is xz = y^2 = y. Thus, Statement I is incorrect. Only Statement II is correct. Answer: II only

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