What is the measure of angle AOB in the circle with center O?

Question

(1) Major arc AB is greater than 180°.
(2) Minor arc AB is 1/11 of the circumference.

Varthini · Answer

B alone is enough to find the minor angle.

1/11 (2. pi.r) = (x° / 360) (2. pi.r)

=> x can be found

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PKN · Answer

Question stem:  \angle{AOB} =?

St1:-  Major arc AB is greater than 180°. 
Greatest measure of an arc of a circle is the measure of circumference, i.e,  2\pi*r 
Given, Major Arc  AB>\pi 
So, \pi <Arc AB < 2\pi*r 
No unique value of arc AB as measure of radius is not known and length of arc AB is a variant.
And measure of  \angle{AOB}  is dependent on the measure of arc AB.
Therefore, insufficient.

St2:-  Minor arc AB is 1/11 of the circumference 
Or, Minor Arc AB= \frac{2\pi*r}{11} 
 \angle{AOB}  formed by minor arc AB= \frac{Arc_{AB}}{Radius} = \frac{\frac{2\pi*r}{11}}{r}=\frac{2\pi}{11}

Sufficient.

Ans. (B)

abhishekrukhaiyar · Answer

The question is asking a definite value. 
1) The information that Major arc is greater than 180° does not give any information which can give definite information about the angle. Hence, insufficient.
2) The arc and angle it forms at the center are directly proportional. For 360°, circumference is 2 \pi r. So, if arc vs circumference ratio is known, angle it is forming at center can be easily calculated. Hence, sufficient. 
Hence, B is correct option.

GMAT215 · Answer

In this question, angle AOB, is ON major arc or minor arc??

If it's major arc angle will be say towards 360 degree. Whereas AOB is made using minor arc, angle will be towards zero..

Question no where specifies which part of circle is to be used... Hence we have two different angles..

So, E may be correct answer.

If u don't agree with this thought process. Pls mention why..

N if I am making some real mistake while thinking this way.. Pls come to rescue

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amanvermagmat · Answer

Hello

My thoughts on your query are these:

The question doesnt ask specifically about minor angle AOB (less than 180 degrees i mean) or major angle AOB (greater than 180 degrees i mean). 
But in any case, from the second statement alone, we would be able to figure out minor angle AOB. If we can figure out minor angle AOB, we can also figure out major angle AOB. So in any case we have our answer with us.

Thats why I think answer should be B.

gvij2017 · Answer

I agree with your explanation but when question stem ask a value then I must have a unique value as solution. 
Here your are getting two values.

In DS, basically two type of question can be seen. 
1. YES/NO TYPE
2. A unique solution/value

So here either answer must be E or question should specify the angle which it is asking-major or minor angle.

anurasi · Answer

Since there is no pictorial representation, O can very well be the center either of major arc or minor arc. Answer should hence be E.

What is the measure of angle AOB in the circle with center O?

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GMAT Data Sufficiency (DS) Questions

What is the measure of angle AOB in the circle with center O?

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