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    Question

    Consider three positive numbers that form a ratio of

    2:3:4. If the sum of the squares of these numbers is 2349, what is the average of the largest and the second largest numbers?
    A 22.5 Correct Answer Incorrect Answer
    B 27.5 Correct Answer Incorrect Answer
    C 31.5 Correct Answer Incorrect Answer
    D 30 Correct Answer Incorrect Answer

    Solution

    Let the three numbers be 2x, 3x and 4x, respectively. ATQ; (2x) 2 + (3x) 2 + (4x) 2 = 2349 Or, 4x2 + 9x2 + 16x2 = 2349 Or, 29x2 = 2349 Or, x2 = 81 So, x = 9 (Since, numbers are positive therefore we can discard the negative root) So, required average = {(3 x 9) + (4 x 9)} ÷ 2 = (63/2) = 31.5 Hence, option c.

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