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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.
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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.
The question asks the value of (4/3) - xy/(x+y) for the following reason
(4x-3xy+4y)/(3x+3y)
= [4(x+y)-3xy]/[3(x+y)]
= [4(x+y)]/[3(x+y)] - [3xy]/[3(x+y)]
= (4/3) - xy/(x+y)
Since we have (x+y)/xy = 3 from condition 2),) for the following reason
(1/x)+(1/y) = 3
(y/xy) + (x/xy) = 3
(x+y)/xy = 3
Then we have xy/(x+y) = 1/3.
Then (4/3) - xy/(x+y) = (4/3) - (1/3) = 1.
Since condition 2) yields a unique solution, it is sufficient.
Condition 1)
Since we have x=y, (4/3) - xy/(x+y) = (4/3) - x^2/2x = (4/3)-x/2.
If x = y = 1, then (4/3) - x/2 = 5/6.
If x = y = 2, then (4/3) - x/2 = 1/3.
Since condition 1) does not yield a unique solution, it is not sufficient.
Therefore, B is the answer.
Answer: B
