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by maihuna » Thu Jul 14, 2011 10:45 am
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?

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Charged up again to beat the beast :)
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by winniethepooh » Thu Jul 14, 2011 11:21 am
Is the OA square feet.
Last edited by winniethepooh on Thu Jul 14, 2011 1:58 pm, edited 1 time in total.
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by GMATGuruNY » Thu Jul 14, 2011 12:37 pm
--
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:

Image

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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by winniethepooh » Thu Jul 14, 2011 1:37 pm
Hey Mitch, many times I have seen experts and members writing that this question is unlikely to appear on the Gmat, but I don't understand what is the basis of such a claim.
Please don't mind answering!
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by GMATGuruNY » Thu Jul 14, 2011 3:41 pm
winniethepooh wrote:Hey Mitch, many times I have seen experts and members writing that this question is unlikely to appear on the Gmat, but I don't understand what is the basis of such a claim.
Please don't mind answering!
It's more than unlikely -- it's certain -- that the question above would not appear on the GMAT.
While the question can be solved by plugging in the answers, the direct solution seems to require that we take the derivative of a quadratic equation in order to determine the equation's maximum value.
Derivatives are beyond the scope of the test.
It's incumbent on me to point this out so that BTGers don't worry about mastering topics that are not tested.
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by winniethepooh » Thu Jul 14, 2011 7:07 pm
Thanks! :)
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