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    Question

    Product of two consecutive positive even numbers is 624.

    Find the sum of the digits of the two numbers.┬а┬а
    A 12 Correct Answer Incorrect Answer
    B 14 Correct Answer Incorrect Answer
    C 16 Correct Answer Incorrect Answer
    D 18 Correct Answer Incorrect Answer

    Solution

    Let the numbers be ( 2n ) and ( (2n + 2) ) respectively.┬а ATQ,┬а ( 2n * (2n + 2) = 624 )┬а Or, ( n * (2n + 2) = 312 )┬а Or, ( 2n┬▓ + 2n = 312 )┬а Or, ( n┬▓ + n = 156 )┬а Or, ( n┬▓ + n - 156 = 0 )┬а Or, ( n┬▓ + 13n - 12n - 156 = 0 )┬а Or, ( n(n + 13) - 12(n + 13) = 0 )┬а Or, ( (n + 13)(n - 12) = 0 )┬а So, ( n = -13 ) or ( 12 )┬а So, ( n = 12 ) So, numbers are ( 24 ) and ( 26 ).┬а Therefore, required sum = ( 2 + 4 + 2 + 6 = 14 )┬а

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