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      Question

      Product of two consecutive positive even numbers is 624.

      Find the sum of the digits of the two numbers.  
      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.  ATQ,  ( 2n * (2n + 2) = 624 )  Or, ( n * (2n + 2) = 312 )  Or, ( 2n² + 2n = 312 )  Or, ( n² + n = 156 )  Or, ( n² + n - 156 = 0 )  Or, ( n² + 13n - 12n - 156 = 0 )  Or, ( n(n + 13) - 12(n + 13) = 0 )  Or, ( (n + 13)(n - 12) = 0 )  So, ( n = -13 ) or ( 12 )  So, ( n = 12 ) So, numbers are ( 24 ) and ( 26 ).  Therefore, required sum = ( 2 + 4 + 2 + 6 = 14 ) 

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