If O is the center of the circle above, what fraction of the circular

Question

https://gmatclub.com/forum/download/file.php?id=18231 If O is the center of the circle above, what fraction of the circular region is shaded? (A) 1/12 (B) 1/9 (C) 1/6 (D) 1/4 (E) 1/3 Circle.png

Bunuel · Answer

SOLUTION

https://gmatclub.com/forum/download/file.php?id=18231 
 If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150°+150°=300° of the circle is not shaded, hence 360°-300°=60° of the circle is shaded, which is  \frac{60}{360}=\frac{1}{6}  of the circular region.

Answer: C.

dexerash · Answer

Total angle in a circle = 360 degree
One of Non-shaded angle = 150 degree
Other Non-shaded angle = 150 degree (?) because it is opposite angle
Total Non-shaded angle = 150 + 150 = 300 degree
So, shaded angle = 360 - 300 = 60 degree

Shaded angle 60
--------------- = ------- = 1/6
Total angle 360

Hence, C

Javoni · Answer

I would say (C), but it seems such an easy answer. Anyways, here is the explanation: 360-2*150=60
60 degrees is the total of shaded regions, so 60/360 = 1/6.
So, please correct me if I went awry.

p.s.
where is trick here?
those shaded regions opposite to each other do not have equal angles?

SOURH7WK · Answer

Since both Lines pass through centers they are alternate angles. Hence shaded degree measure is 360- (150x2)=60

So fraction of circle shaded = 60/360 = 1/6.

Hence Answer Choice C.

fameatop · Answer

Fraction of Shaded region = Angle made at the center by shaded region/ Angle at center of a circle
 = (360-150*2)/360 = 60/360 = 1/6
 Answer C

Bunuel · Answer

SOLUTION

https://gmatclub.com/forum/download/file.php?id=18231 
 If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150° + 150° = 300° of the circle is NOT shaded, hence 360° - 300° = 60° of the circle IS shaded, which is  \frac{60}{360}=\frac{1}{6}  of the circular region.

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

subirh · Answer

Part of circle not shaded=150+150=300. So, shaded part is 360-300=60.
Required fraction is :60/360=1/6

luckyme17187 · Answer

not shaded is 150+150 =300.

so shaded has to be 360-300= 60..

60/360 = 1/6.

mcelroytutoring · Answer

Attached is a visual that should help.

ScottTargetTestPrep · Answer

In solving this problem there are three angle rules that we must consider.

1) A circle measures a total of 360 degrees.

2) A straight angle measures 180 degrees.

3) Vertical angles, angles that are directly opposite one another, are always equal.

To solve, we can draw out a quick diagram of just the angles:

https://i.imgur.com/fabjDmz.png

Based on the angles we created, we know two important pieces of information:

1) angle A and 150 degrees sum to 180 degrees because they form a straight angle. Thus, angle A = 30 degrees.

2) angle A = angle B because they are vertical angles. Thus angle B = 30 degrees.

With this information we see that the shaded region represents 60 out of 360 degrees of the circle, or 60/360 = 1/6.

The answer is C.

diegocml · Answer

Given: The angle opposite the 150 degree angle has the same measure.

Call x = each of of the shaded regions

2(150) + 2x = 360
300 + 2x = 360
2x = 60
x = 30

Sum of the angles of the shaded regions = 60 degrees

60/360 = 1/6

Answer choice  C

Jamie007 · Answer

Non shaded angle = 300 degree.

Shaded angle = 360-300 = 60 degree.
Fraction = 60/360 = 1/6.

Answer C

sasyaharry · Answer

We can also say area of each shaded portion is  \frac{30*\pi*r^{2}}{360}  =  \frac{\pi*r^{2}}{12}  
Area of 2 shaded portions = 2 *  \frac{\pi*r^{2}}{12}  =  \frac{\pi*r^{2}}{6}

Ratio is  \frac{Area of shaded portions}{Area of circle}  =  \frac{1}{6}

Shiv2016 · Answer

Bunuel  I solved this question using the sector formula. I found this angle method really simple. In what all cases can we use it?

dave13 · Answer

Hello Bunuel why didnt my simple proporttion method work here

360 = 100% 300 = x

Bunuel · Answer

The shaded region is 60 degrees not 300.

rishabhmishra · Answer

IMO C  whole circle has 360 degree and as opposite angles are equal then opposite angle to 150 is also 150 and unshaded region is 300 
shaded region is 60 so area of sector = 60/360pie r^2 which is 1/6pie r^2 and total are is pie r^2 so 1/6pie r^2/ pie r^2 = 1/6

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If O is the center of the circle above, what fraction of the circular

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If O is the center of the circle above, what fraction of the circular

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards