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maihuna wrote:The riding stables has just received an unexpected rush of registrations for the next horse show, and quickly needs to create some additional paddock space. There is sufficient funding to rent 1200 feet of temporary chain-link fencing. The plan is to form two paddocks with one shared fence running down the middle. What is the maximum area that the stables can obtain?
100
150
200
220
250
The answers represent not the area but the WIDTH of the
paddock (a strange word unlikely to appear on the GMAT).
Here is a drawing of the paddock:
The GMAT-friendly way to solve would be to plug in the answers.
Answer choice C: W = 200
Thus, L = 600 - (3/2)200 = 300.
Area = 200*300 = 60,000.
Each of the remaining answers will yield a smaller area.
The correct answer is
C.
The direct solution involves taking the derivative of a quadratic.
Derivatives are not tested on the GMAT.
For the curious:
A = W * (600 - 3/2W)
= 600W - (3/2)W²
The derivative of the quadratic above is 600 - 3W.
The quadratic is maximized when the derivative equals 0:
600 - 3W = 0
W = 200.
I wouldn't worry about this question. It would never appear on the GMAT.
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