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    Question

    Product of two consecutive positive even numbers is 840.

    Find the sum of the digits of the two numbers.  
    A 11 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 13 Correct Answer Incorrect Answer
    D 14 Correct Answer Incorrect Answer

    Solution

    Let the numbers be ( 2n ) and ( (2n + 2) ) respectively.  ATQ,  ( 2n * (2n + 2) = 840 )  Or, ( n * (2n + 2) = 420 )  Or, ( 2n² + 2n = 420 )  Or, ( n² + n = 210 )  Or, ( n² + n - 210 = 0 )  Or, ( n² + 15n - 14n - 210 = 0 )  Or, ( n(n + 15) - 14(n + 15) = 0 )  Or, ( (n + 15)(n - 14) = 0 )  So, ( n = -15 ) or ( 14 )  So, ( n = 14 )  So, numbers are 28  and 30.  Therefore, required sum = ( 2 + 8 + 3 + 0 = 13 ) 

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