[GMAT math practice question]

Working alone at its constant rate, machine A can produce 240 pins in x hours. Working alone at its constant rate, machine B can produce 240 pins in y hours. How many hours will it take machines A and B to produce 240 pins, when working together at their respective constant rates?

1) \(\frac{xy}{(x+y)}=4\)
2) \(x=20\)
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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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We have \(\frac{1}{t} = \frac{1}{x} + \frac{1}{y} = \frac{(x+y)}{xy}\) or \(t = \frac{xy}{(x+y)}\), where t is the time that machines A and B take to produce 240 pins, when working together. The question asks for \(\frac{xy}{(x+y)}\).

Thus, only condition 1) is sufficient. Condition 2) is not sufficient as it only gives us information about \(x\).

Therefore, the answer is A.
Answer: A
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