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    Question

    The sum of three positive numbers is 18 and their

    product is 162. If the sum of two numbers is equal to the third then the sum of squares of the numbers is
    A 120 Correct Answer Incorrect Answer
    B 126 Correct Answer Incorrect Answer
    C 132 Correct Answer Incorrect Answer
    D 138 Correct Answer Incorrect Answer

    Solution

    Let us consider the three positive numbers as x, y and z. Sum of three positive numbers x + y + z = 18 ---------> (1) product of three numbers xyz=162 ----------> (2) Given that sum of two numbers is equal to the third. i.e.., x + y = z => 2z = 18 => z = 9 Replacing z=9 in equation (1) & (2), we get x + y = 9 and xy = 18 Solving above, we get x = 6 and y = 3 therefore, sum of squares of the numbers = 62 + 32 + 92 = 126

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