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 Post subject: GMAT GeometryPosted: Wed Mar 09, 2011 4:57 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424

The figure above represents two tangential wheels touching one another at exactly one point. The larger wheel has a circumference of 6π and the smaller wheel has a circumference of 4π. If x and y are the centers of the wheels, what is the distance from point x to point y?

A. 5
B. 6
C. 10
D. 12
E. 15

(A) This question is essentially just asking for the sum of the two radii, since the wheels are touching.

Since circumference = 2πr, radius = circumference/2π. Thus, the smaller wheel has a radius of 4π/2π = 2 and the larger wheel has a radius of 6π/2π = 3.

The distance between x and y is 2 + 3 = 5. The correct answer is choice (A).
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What is the difference between the number of revolutions the two gears make per minute?

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 Post subject: Re: GMAT GeometryPosted: Wed Mar 09, 2011 5:50 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Though this information is irrelevant to this particular question, let us analyze what happens when wheels rotate.

Imagine the both wheels roll on a line (connected as they are). When the larger one makes a full turn, the wheels will travel the distance of its circumference, or 6π. Therefore the smallest wheel will turn once to travel 4π, plus half a turn to travel 2π. (4π + 2π = 6π). That's the logic that stands behind the following rule.

Knowing the circumferences, we can find the ratio between revolutions per minute. If the larger wheel rotates at x rmp, and the smaller wheel rotates at y rpm, then the ratio of rpm's is a reciprocal of the ratio of their circumferences:

x/y = 4π/(6π) = 2/3

So for every 2 revolutions that the larger wheel makes, the smaller one revolves 3 times.

Therefore we know the ratio between rpm, but we don't know the actual difference, since we need to know the rotation speed of at least one of the wheels.

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