Data Sufficiency

[GMAT math practice question]

What is the value of xy?

1) x^2-4xy+5y^2-4xy+4 = 0
2) |x-4| = - √(y-2)

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1)
x^2-4xy+5y^2-4xy+4 = 0
=> x^2-4xy+4y^2+y^2-4xy+4 = 0
=> (x-2y)^2 + (y-2)^2 = 0
=> x = 2y and y =2, since (x-2y)^2 ≥ 0 and (y-2)^2 ≥ 0.
So, x = 4 and y =2. Thus, xy = 8.
Condition 1) is sufficient since it yields a unique solution.

Condition 2)
|x-4| = - √(y-2)
=> |x-4| +√(y-2) = 0
=> |x-4| = 0 and √(y-2) = 0, since |x-4| ≥ 0 and √(y-2) ≥ 0.
So, x = 4 and y =2. Thus, xy = 8.
Condition 2) is sufficient since it yields a unique solution.

Therefore, D is the answer.
Answer: D