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09 Dec 2021, 02:20
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Five identical circles shown above have their centers equally spaced on a straight horizontal line. Another line connects the bottom of the first circle and the top of the fifth circle. If the area of the grey region, under the line enclosed by the circles, is equal to 40 and the overlapping area between any two adjacent circles is equal to 5. What is the area of one circle?
A. \(12\)
B. \(20\)
C. \(25\)
D. \(30\)
E. \(60\)
09 Dec 2021, 02:20
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Official Solution:
Five identical circles shown above have their centers equally spaced on a straight horizontal line. Another line connects the bottom of the first circle and the top of the fifth circle. If the area of the grey region, under the line enclosed by the circles, is equal to 40 and the overlapping area between any two adjacent circles is equal to 5. What is the area of one circle?
A. \(12\)
B. \(20\)
C. \(25\)
D. \(30\)
E. \(60\)
The figure given is symmetrical around the line crossing it, so if the area of the grey region is 40, then the area of the whole figure is 80.
The total area of five circles IF they were not overlapping would be the area of the figure PLUS four times the area of one overlap (each of the four overlaps belong to two circles). So, the area of five circles is \(80 + 4*5=100\). The area of one circle is therefore, 20.
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. You do not need to calculate the area of the circle, even if you may have wanted to. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: B
Five identical circles shown above have their centers equally spaced on a straight horizontal line. Another line connects the bottom of the first circle and the top of the fifth circle. If the area of the grey region, under the line enclosed by the circles, is equal to 40 and the overlapping area between any two adjacent circles is equal to 5. What is the area of one circle?
A. \(12\)
B. \(20\)
C. \(25\)
D. \(30\)
E. \(60\)
The figure given is symmetrical around the line crossing it, so if the area of the grey region is 40, then the area of the whole figure is 80.
The total area of five circles IF they were not overlapping would be the area of the figure PLUS four times the area of one overlap (each of the four overlaps belong to two circles). So, the area of five circles is \(80 + 4*5=100\). The area of one circle is therefore, 20.
Note that while this question uses basic knowledge of lines and figures, it is actually not a Geometry question. You do not need to calculate the area of the circle, even if you may have wanted to. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: B
