Question 15. For each of the three circles shown above, the diameter of the smaller circle is equal to the radius of the larger. If the radius of the largest circle is equal to 8 inches, what is the area of the shaded region? A. 3π. B. 6π. C. 12π. D. 15π. E. 18π.
(C) The first step is to understand the strategy. We have to find the area of the entire black circle and subtract from it the area of the smallest circle.
Since we know that the largest circle has a radius of 8, the black circle must have a radius of 4 and the smallest circle must have a radius of 2. The area of the smallest circle is equal to: πR² = π2² = 4π. Now, we want to find the area of the black circle: πR² = π4² = 16π. Finally, we subtract the smaller area from the area of the black circle to get 16π - 4π = 12π, or answer choice (C).
it does not seem to be possible to infer from the information given in the question that radii relate 2:4:8, unless we assume that diameter of the black circle is equal to the radius of the largest circle. i do not see how we can assume that
Post subject: Re: Math: test 2, question 15 (Geometry)
Posted: Fri Apr 16, 2010 10:41 am
Joined: Fri Apr 09, 2010 2:11 pm Posts: 401
When solving any question on GMAT it is very important to read the question statement very carefully, because missing just one word can be very crusial.
The statement itself tells us that "For each of the three circles shown above, the diameter of the smaller circle is equal to the radius of the larger." so we do not need to assume that diameter of the black circle is equal to the radius of the largest circle. This information is given to us.
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