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    Question

    Given below are two statements Statement I

    : The given set of numbers (5,6,7,p,6,7,8,q) has an arithmetic mean of 6, and its mode (the number occurring most frequently) is 7. Additionally, it is known that p × q = 16. Statement II : Let p and q be two positive integers such that p + p × q = 94. Then p + q = 20. In light of the above statements, choose the correct answer from the options given below.
    A Both statement I and II are true Correct Answer Incorrect Answer
    B Both statement I and II are false Correct Answer Incorrect Answer
    C Statement I is true but Statement II is false Correct Answer Incorrect Answer
    D State I is false but Statement II is true Correct Answer Incorrect Answer

    Solution

    Mean- The mean is the average or the most common value in a collection of numbers. In Statement I, For p × q = 16; the possible pairs are (4, 4); (8, 2); (16, 1); but by no pair can we ensure a mean of 6 In Statement II, The first equation can be simplified as q(p + 1) = 94 and the other one can be written as p + q = 20 But these 2 equations are not consistent. There can be no pair of p and q that satisfies the equations. ∴ This statement is also wrong.

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