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    A set of fifteen numbers has an arithmetic mean of 42 . The mean of the first eight numbers is 39 , while the mean of the last eight numbers is 44 . T
    Question

    A set of fifteen numbers has an arithmetic mean of 42 . The mean of the first eight numbers is 39 , while the mean of the last eight numbers is 44 . The value of the eighth number is

    A.

    36

    B.

    32

    C.

    34

    D.

    38

    Correct option is C

    Given:
    Mean of 15 numbers = 42
    Mean of first 8 numbers = 39
    Mean of last 8 numbers = 44
    Formula Used:
    Sum = Mean × Number of observations
    Overlapping term = (Sum of first n terms + Sum of last n terms) - Total Sum
    Solution:
    Calculate the total sum of all 15 numbers.
    Total Sum = 15 × 42 = 630
    Calculate the sum of the first 8 numbers.
    Sum of first 8 = 8 × 39 = 312
    Calculate the sum of the last 8 numbers.
    Sum of last 8 = 8 × 44 = 352
    Since the 8th number is counted twice (once in the first 8 and once in the last 8), we can find its value by adding the two subgroup sums and subtracting the total sum.
    Value of 8th number = 312 + 352 - 630
    Value of 8th number = 664 - 630 = 34
    Final Answer
    So the correct answer is (c)

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