niheil wrote:
The perimeter of a rectangular garden is 360 feet. What is the length of the garden?
(1) The length of the garden is twice the width.
(2) The difference between the length and width of the garden is 60 feet.
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Let l and w be the length and the width of the rectangular garden, respectively.
From the original condition of the question, we have \(2(l+w) = 360\) or \(l + w = 180\).
There are 2 variables and 1 equation. Thus D is the answer most likely.
Condition 1) \(l = 2w\)
\(l + w = 2w + w = 3w = 180\) or \(w = 60\).
Thus \(l = 120\).
It is sufficient.
Condition 2) \(l - w = 60\), since the length is the longest side of a rectangle.
When we add two equations, \(l + w = 180\) and \(l - w = 60\), we have \(2l = 240\) or \(l = 120\).
It is sufficient.
Therefore the answer is D.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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