Problem Solving

please help me out with this question. its on the kaplan software Data sufficency
Thanks

For Area of shaded region, we need to subtract the area of sector from the area of circle..

For area of sector, we need the angle subtended AND the radius.

2 tells us angle is 60
1 gives us the radius.
C

Area of the shaded region?

= (Angle MON)/360 * (pi)* r^2

So you need Angle O and value of r?

Statement 1
circumference = 2*pi*r
2*pi*r = 30

you can find the value of r
but you dont know value of Angle O

Insufficient

Statement 2
MN = NO = OM

Angle O = 60 degrees
but we have no idea about value of r

Insufficient


But combining the two..
we know value of r and angle MON
and thus we can find the Area of the shaded region.


OptionC

Area of shaded region = Area of circle - Area of Sector

1)Gives area of circle but nothing about sector.Not sufficient.
2)Each angle of triangle =60.
Thus area of sector = 60/360 * Area of circle.
Not sufficient.

Combining you can solve the question.Do not calculate the actual answer.OA is C

IMO C

angle MON/360 * pi * r ^2 = ?

1.Gives r, no info on angle MON.
2.Give angle MON, no info on radius

Combining both we can get the answer.