Bunuel wrote:
Working together, Max and Mandy painted the living room in six hours. How long would it have taken for Max to paint the room by himself?
(1) Mandy paints twice as fast as Max does.
(2) If Max had left when the job was half finished, it would have taken Mandy hours 4 1/2 to finish the job by herself.
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.
Assume \(x\) and \(y\) are times Max and Mandy take to paint the room alone, respectively.
Then we have \(\frac{1}{x} + \frac{1}{y} = \frac{1}{6}\).
Since we have 2 variables (\(x\) and \(y\)) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since \(y = \frac{1}{2}x\) or \(x = 2y\), we have \(\frac{1}{x} + \frac{1}{y} = \frac{1}{{2y}} + \frac{1}{y} = \frac{3}{{2y}} = \frac{1}{6}\) or \(2y = 18\).
Thus, we have \(x = 18\) and \(y = 9\).
Since condition 1) yields a unique solution, it is sufficient.
Condition 2)
Since Mandy has taken \(4\frac{1}{2}\) hours to finish half the job, we have \(y = 2 \cdot 4.5 = 9\).
Then we have \(x = 2y = 2 \cdot 9 = 18\).
Since condition 2) yields a unique solution, it is sufficient.
Therefore, D is the answer.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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