Video Explanation

Text Explanation

Using a tried and true DS strategy, start with the easier statement, Statement #2.

Statement #2:

(y – 4)(y + 2) = 0

y = +4 or y = –2

Since there are two values of y, this statement, alone and by itself, is not sufficient. 

Statement #1:

This is an equation with a radical.  The radical is already isolated, so square both sides. 

(3y – 1)² = 8y² – 4y + 9

9y² – 6y + 1 = 8y² – 4y + 9

y² – 2y – 8 = 0

Lo and behold!  We have arrived at the same equation we found in Statement #2, with solutions y = +4 or y = –2.  The naïve conclusion would be—this statement says exactly the same thing as the other.  That's incorrect, though, because we don't know whether both of these values are valid solutions, or whether one or more is an extraneous root.  We need to test this in the original equation. 

Test y = +4

Left side: 

Right side: 

This value checks: y=+4 is a valid solution to the equation

Test y = –2

Right side: 

The two sides are not equal, so this does not check!  This value, y = –2, is an extraneous root. 

(NB: it's often the case that an extraneous root will make the two sides equal to values equal in absolute value and opposite in sign.) 

Thus, the equation given in Statement #1 has only one solution, y = 4, so this equation provides a definitive answer to the prompt question.  This statement, alone and by itself, is sufficient. 

Answer = (A)