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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the diagram above, O is the center of the circle and angle AOB = 14

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Math Expert V
Joined: 02 Sep 2009
Posts: 58423
In the diagram above, O is the center of the circle and angle AOB = 14  [#permalink]

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In the diagram above, O is the center of the circle and angle AOB = 144º. What is the area of the circle?

(1) The area of sector AOB is 40% of the area of the circle
(2) Arc ACB has a length of $$14\pi$$.

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Re: In the diagram above, O is the center of the circle and angle AOB = 14  [#permalink]

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the answer is B

statment 1:The area of sector AOB = 40/100= 2/5 of the area of the circle

The area of sector =the area of the circle*N/360

2/5 pi.= pi*N/360

2/5pir^2 = 144/360 pir^2

2/5pir^2 = 2/5 pir^2

so statment 1 is insuff where no new information we can get from statment 1

Statment 2

length of the Arc =2rpi*N/360

14r=2pir*144/360
14/r= 2/5
r=35/2
r=17.5
so we can find the area of the circle
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Math Expert V
Joined: 02 Sep 2009
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In the diagram above, O is the center of the circle and angle AOB = 14  [#permalink]

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Bunuel wrote: In the diagram above, O is the center of the circle and angle AOB = 144º. What is the area of the circle?

(1) The area of sector AOB is 40% of the area of the circle
(2) Arc ACB has a length of $$14\pi$$.

MAGOOSH OFFICIAL SOLUTION:

First of all, we should think about the prompt a bit. This angle, 144º, is what fraction of a full circle? Well, both 144 and 360 are divisible by 4: 144 ÷ 4 = 36 and 360 ÷ 4 = 90, so 144/360 = 2/5.

This angle is 2/5 of the whole circle, so the arc is 2/5 of the whole circumference. Also, remember that if we can find anything about the whole circle, for example, the circumference, then we can find the radius, which would allow us to find the area.

Statement #1: This is a tautological statement. A tautological statement is a statement that, by definition, has to be true, and because of this, it contains no information. Statements such as “My car is a car” and “My employer employs me” are verbal tautologies: they contain no useful information. Much in the same way, we already know from the prompt that the angle takes up 2/5 of the circle, so of course the sector would take up 2/5, or 40%, of the area. This statement repeats information in the prompt, and contains no new information, so it doesn’t help us at all to figure out anything else. This statement, alone and by itself, is not sufficient.

Statement #2: We already know this arc is 2/5 of the whole circumference, so we could set up a proportion to find the circumference. From that, we could find the radius, and that would allow us to find the area. This statement, alone and by itself, is sufficient.

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Re: In the diagram above, O is the center of the circle and angle AOB = 14  [#permalink]

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Statement 1 is actually restatement of question stem and provides no new information
(144/360) * 100 = 40%
clearly insufficient
Statement 2 provides us information on length of arc ACB from which we can find the circumference and thus the radius and eventually the area of circle So clearly Sufficient
Correct answer - B

P.S. Don't waste time in exam in actually calculating the area of circle
Director  G
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Re: In the diagram above, O is the center of the circle and angle AOB = 14  [#permalink]

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Bunuel wrote:
Attachment:
cpotg_img1-284x300.png
In the diagram above, O is the center of the circle and angle AOB = 144º. What is the area of the circle?

(1) The area of sector AOB is 40% of the area of the circle
(2) Arc ACB has a length of $$14\pi$$.

So area of the circle = $$\pi * r^2$$

from 1) Area of sector = 40/100 * area of circle
But radius is not given, thereby making this insufficient.

from 2) Arc ACB has a length of $$14\pi$$

from this length we can get the radius using the length of the arc formula.

Radius can be used to get the area of the circle.

B
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: In the diagram above, O is the center of the circle and angle AOB = 14   [#permalink] 07 Feb 2019, 07:35
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In the diagram above, O is the center of the circle and angle AOB = 14

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