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555-605 (Medium)|   Geometry|      
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amanvermagmat
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AB and CD are both diameters of a circle with centre O. So A, B, C, D 04 Jul 2018, 23:20
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

79% (01:36) correct 21% (01:45) wrong based on 44 sessions

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AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.
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D
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AB and CD are both diameters of a circle with centre O. So A, B, C, D 04 Jul 2018, 23:53
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amanvermagmat
AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.
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Questions like these, which talk about a figure without giving it, are much easier to answer if we draw them out first.
This is an Alternative approach.

(1) Drawing a circle with two diameters and writing in AOD = 100, we can fill the angle opposite to it to be 100. Since the 4 angles sum to 360, the remaining two sum to 360 - 200 = 160.
So sectors AOC and BOD are proportional to 160 degrees of the circle meaning they have 160/360 of the area.
Sufficient.

(2) repeating the same process as above gives us exactly the same values.
Sufficient.

(D) is our answer.
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AB and CD are both diameters of a circle with centre O. So A, B, C, D 05 Jul 2018, 01:04
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amanvermagmat
AB and CD are both diameters of a circle with centre O. So A, B, C, D all lie on the circumference of the circle. Sum of areas of sector AOC and sector BOD is what fraction of the total area of the circle?

(1) Angle AOD = 100 degrees.

(2) Angle AOC = 80 degrees.
Show more


Please refer the affixed diagram for the explanation.

Both statements are alone sufficient.

Ans. (D)
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Sector.JPG
Sector.JPG [ 34.55 KiB | Viewed 2569 times ]

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