You may consider another logic/solution.


If the numbers are in the ratio 2 to 7, it means that one number is 2x, while another number is 7x, where x is an unknown factor.


Then the product of these numbers is  (2x)*(7x) = 14x^2.

At the same time, the product is 126, according to the condition.  


It gives you an equation  14x^2 = 126.


Hence,  x^2 =  = 9.


It implies  x = +/-  = +/- 3.


If x = 3,   then your answer is: the two numbers are  2*3 = 6  and  7*3 = 21.
                          The greatest of the two numbers is 21.


If x = -3,  then your answer is: the two numbers are  2*(-3) = -6  and  7*(-3) = -21.
                          In this case the greatest of the two numbers is -6.


Answer.  There are two answers to the problem's question: -6  and  21.

Correct answer:  

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