How to Find the Core Concept in GMAT Geometry (Circles and Perimeter)

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Hi GMATters,

This is a great example of a question that looks a lot more difficult than it really is.

You'll find that most Geometry questions tend to rely on one core concept. Everything else is a bit of an afterthought.

What do I mean by that?

Simple: look at this question. Noting that...

1) the radius of the circle is r

2) all of the answers have pi*r^2 in them

...it's actually pretty easy to see that we don't really need to worry about the area of the circle. I mean that assumes you know that pi*r^2 is the area of a circle, but if that's the case then I'm afraid you have bigger problems on your plate than what we're addressing in this question.

Next, we have to consider what's left.

Think about this: the length that is taken out of the main wire by the circle is the "flat length" of the circle.

Imagine taking a bicycle tire and cutting it at its center and laying that flat. That's what I mean by "flat length." If you really wanted to use icky math terms, you could call that "circumference."

So... the amount of the wire that's not the circle is:

total - circumference of circle

And this is what creates all four sides of the square. That's the perimeter of the square, of course.

So divide that by four to get the side length of the square.

If you take that side length and square it, you get the area of the square. Hmm... is that why they call it "squaring?" Worth pondering...

Happy GMATting,

Rowan

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A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

A. π∗r2π∗r2
B. π∗r2+10π∗r2+10
C. π∗r2+14∗π2∗r2π∗r2+14∗π2∗r2
D. π∗r2+(40−2π∗r)2π∗r2+(40−2π∗r)2
E. π∗r2+(10−12π∗r)2