GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750


If an x meter long rope can enclose (or cover) a maximum area of 50 square meters, what is the approximate length of the rope?

A. 4
B. 7
C. 10
D. 20
E. 25
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A square could be larger?

x^2 = 50

x = (5)*\sqrt{2}

Perimeter = (20)*\sqrt{2} = (20)*(1.4) \approx 28

Exactly.

Circle:- If 25 meter of rope can cover a circle with an area of 50 sq meter, then 28 meter of rope can cover a circle with an area of >50 sq. meter.

Square:- If 28 meter of rope can cover a square with an area of 50 sq meter, then 25 meter of rope can cover a square with an area of <50 sq. meter.

Therefore, Circle is correct.
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GT

Re-read the question:- It says "a maximum of".


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GT

Agreed. When I read "cover" I was first just thinking about the actual surface area of the ground covered by the rope itself, not the amount of spaced enclosed by the shape made with the rope.

I might be in the minority, however...

is this the modified question and explanation

The revised wording:


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GT

Tiger, what is about the minimum area covered of a given length?
I supposed it to be a triangle, and then with the increasing of the number of angles, the covered area is increasing.
What do you think about it?

my 2 cents. it is tough question unless you know than for a ginven length of rope the maximum covered area is a circle, otherwise it would not be of 750 level.
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I believe "cover" is confusing. It would be better to just leave "enclose". Nice question thank you!

lol, spending more time trying to interpret the English over the math is not helpful. I think its obvious the wording is just misleading; although the concept is clear. So rather than criticize, I think its important to ask what exactly the question is trying to test? And then re-word around that aim, without spelling it out.

the word "enclose" can be interpreted as meaning to surround, and the word "cover" means something totally different (as if laying a sheet over something to cover it)... "cover" should not be in there.

For a rope to "enclose" a 'maximum' area of 50 square metres, the question itself is telling us that this rope can "enclose", for example, a rectangular garden that is 50m x 1m, in which case the rope must be 102m long.. obviously this changes per each dimension of the object that might be visualized (square, triangle, rectangle, circle, etc.), but the question doesn't clarify this to the reader in terms of what's being asked. This is where the word "maximum" might be misleading and perhaps overlooked.

- clearly a 102-m rope is the minimum length of rope required to enclose a 50m x 1m garden, but if this same length of rope is used to cover a circular garden, it can cover much more than 50 square meters; which goes against the restriction of "maximum area of 50 square meters"

- It's clear that the concept being tested is the ability to identify that a circle is the optimal shape for area maximization.

thus, I would suggest that the question be re-worded to ask:

Which of the following is the approximate minimum length of rope required to enclose an area of 50 square meters.

this would better direct the reader into understanding that the question is looking for you to determine the smallest length of rope to achieve an area of 50 square meters... Those who don't think beyond a square box, will come up with the wrong length, and those who realise that a "50 square meter" area can come in many shapes will realise that a circular enclosure requires the least length of rope.