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    Question

    Product of two consecutive positive even numbers is 624.

    Find the sum of the digits of the two numbers.ย ย 
    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.ย  ATQ,ย  ( 2n * (2n + 2) = 624 )ย  Or, ( n * (2n + 2) = 312 )ย  Or, ( 2nยฒ + 2n = 312 )ย  Or, ( nยฒ + n = 156 )ย  Or, ( nยฒ + n - 156 = 0 )ย  Or, ( nยฒ + 13n - 12n - 156 = 0 )ย  Or, ( n(n + 13) - 12(n + 13) = 0 )ย  Or, ( (n + 13)(n - 12) = 0 )ย  So, ( n = -13 ) or ( 12 )ย  So, ( n = 12 ) So, numbers are ( 24 ) and ( 26 ).ย  Therefore, required sum = ( 2 + 4 + 2 + 6 = 14 )ย 

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