In the figure above, what fraction of the circle with center O is shaded?
A. 1/8
B. 1/4
C. 2/3
D. 3/4
E. 5/6
[spoiler]OA=D[/spoiler]
Source: Princeton Review
In the figure above, what fraction of the circle with center
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Gmat_mission
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In the figure above, what fraction of the circle with center O is shaded?
A. 1/8
B. 1/4
C. 2/3
D. 3/4
E. 5/6
[spoiler]OA=D[/spoiler]
Source: Princeton Review
GMAT/MBA Expert
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ceilidh.erickson
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Angles opposite one another have the same measurement. Thus, both non-shaded regions measure 45 degrees from the center of the circle, for a total of 90 degrees.
A circle is 360 degrees, so 90 degrees is 1/4 of the circle that is unshaded. That leaves 3/4 of the circle shaded.
The answer is D.
A circle is 360 degrees, so 90 degrees is 1/4 of the circle that is unshaded. That leaves 3/4 of the circle shaded.
The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Since the central angle of each white region is 45 degrees, the central angle of each shaded region is 180 - 45 = 135. Thus, (135 + 135)/360 = 270/360 = 3/4 is shaded.Gmat_mission wrote:
In the figure above, what fraction of the circle with center O is shaded?
A. 1/8
B. 1/4
C. 2/3
D. 3/4
E. 5/6
[spoiler]OA=D[/spoiler]
Source: Princeton Review
Alternate Solution:
A sector corresponding to 45° will have an area which is 1/8 of the complete circle. The unshaded region consists of two such sectors; therefore, the unshaded region is 1/8 + 1/8 = 1/4 of the whole circle. Thus, the shaded region is 1 - 1/4 = 3/4 of the whole circle.
Answer: D
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