Crazy GMAT Circles (Easier Than You Think)

by on March 8th, 2017

geometryFor this week’s tip, let’s talk about circles. You may struggle to remember anything around circles beyond they are round and are the shape of the bicycle or car wheels that get you to from point A to point B. Or, in some cases, the spinning wheel of death on a Macbook!

For the GMAT, circles require you know a few key concepts and formulas:

Diameter – the straight-line distance from each side of the circle that passes through the center of the circle

Radius – half the diameter

Circumference = 2{pi}(radius) OR {pi}(diameter)

Area = {pi}(r^2)

There are also more complex problems, like those that include cords or the central angle theorem, but understanding the basics surrounding formulas is an essential first step. We’ll address the advanced stuff in a later post.

Let’s dive right into a tricky Data Sufficiency circle question:

Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to 16 + 16sqrt{2}{pi}?

Statement 1: The radius of one of the small circles is 8

Statement 2: The area of all four circles is 256{pi}

Yikes, right? The key you is that you need to know whether the information provided is workable for you to get to an answer, as well as understanding how you need to look at the figure to determine a path forward.

Redrawing the figure can provide some hints:

As can filling in some additional information:

Hopefully, by now, you have recognized that you simply need the radius of one of the smaller circles to determine the answer to this Data Sufficiency question. In evaluating Statement 1, the radius is given—sufficient. For Statement 2, we simple need to determine if the radius can be found, and if it matches up with Statement 1. 256/4 gives us that each small circle’s area is 64{pi}. If the radius is 8, then the area formula {pi}(r^2) gives us 64{pi}. Statement 2 is also sufficient. The correct answer is (D).

For a good chunk of our circle problems, not crazy calculations are necessary. Remembering the basics of diameter, radius, area, and circumference can get you very far on these questions.

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