Source: Revised GRE PDF 2nd Ed. Section 5; #4 (p. 76)

1

Three circles with their centers on line segment

Three circles with their centers on line segment PQ are tangent at points P, R, and Q, where point R lies on line segment PQ. Quantity A: The circumference of the largest circle Quantity B: The sum of the circumferences of the two smaller circles Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

2 Explanations

2

Dannialles Dominguez

What does it mean that the points P, Q, R are tangent points? The thing that made me skeptical in choosing numbers for this problem is that even though the circles seem to be next to each other, they could not be. In other words , the space where it seems they meet at R could have a gap between them and therefore the two quantities would not be equal. How do I know for sure that this is not the case?

Jan 20, 2014 • Comment

Kevin Rocci, Magoosh Tutor

Hi there! I think you might have answered your own question. Saying that the points P, Q, and R tangent, means that the circles touch at these points. So there is not gap or space between the circles. This is definitely a good thing to keep in mind because sometimes the picture can be misleading, but with the information about tangent points, then we can safely assume that the picture is accurate. :)

Jan 23, 2014

2

Gravatar Chris Lele, Magoosh Tutor

Sep 27, 2012 • Comment

Robert Paul

I would have gotten this wrong because I would think every time you add the circumference of multiple circles you'd do (4pi + 2pi) or (7pi + 3pi) or in other words (4 + 3.14 + 2 + 3.14) or (7 + 3.14 + 3 + 3.14). I'd add additional pi's. Good to know!

Sep 12, 2014

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh