Last visit was: 14 Dec 2024, 09:53 It is currently 14 Dec 2024, 09:53
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
685,831
 []
Given Kudos: 88,270
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,831
 []
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
msk0657
User avatar
Retired Moderator
Joined: 26 Nov 2012
Last visit: 14 Feb 2020
Posts: 472
Own Kudos:
Given Kudos: 46
Posts: 472
Kudos: 524
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
Stn
Joined: 20 Dec 2014
Last visit: 07 Apr 2017
Posts: 29
Own Kudos:
Given Kudos: 3
Posts: 29
Kudos: 50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
MarkusKarl
Joined: 15 Mar 2015
Last visit: 22 Oct 2017
Posts: 88
Own Kudos:
Given Kudos: 7
Posts: 88
Kudos: 65
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I Agree with the previous post. We do not know if O is the center and can thus not solve for the area.

Answer: E

Posted from my mobile device
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
Given Kudos: 88,270
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,831
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Stn
It might be wrong, but...do we know that O is the center to conclude that OA=OB ?

Edited to make that clear.
User avatar
MarkusKarl
Joined: 15 Mar 2015
Last visit: 22 Oct 2017
Posts: 88
Own Kudos:
Given Kudos: 7
Posts: 88
Kudos: 65
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Stn
It might be wrong, but...do we know that O is the center to conclude that OA=OB ?

Edited to make that clear.

In that case:

(1) Tells us the diameter of the circle and thus allows us to calculate a range of measurements of the circle. Area is one of those measurements.
However, we have got no information about the shaded area and are thus unable to answer the question.

Not sufficient.

(2) Due to the fact that the lines inside the circles cut through the diameter we will have two pairs of angles of equal measurement. The angles will add up to 360 degrees. In this case we can calculate the portion of the circle that is shaded. But we do not know how large the circle is.

Not sufficient.

(1)+(2) As we know the area of the circle from (1) and the part/whole-relationship between the shaded area and the circle from (2) we can answer the question.

Answer: C

edit:
Another question about assumptions:
Can we assume that we are dealing with only two lines in this question? Couldn't O connect to 4 lines that do not extend each other?
User avatar
AbdurRakib
Joined: 11 May 2014
Last visit: 14 May 2024
Posts: 472
Own Kudos:
40,536
 []
Given Kudos: 220
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE:Business Development (Real Estate)
Posts: 472
Kudos: 40,536
 []
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure above, if O is the center of the circle, what is the area of the shaded region?

(1) AB = 8
(2) Angle AOR = 45°.

Attachment:
2016-08-17_1248.png

(1) AB=8 ; S, area of the circle=\(\pi 4^2\)=16\(\pi\) ,No information about th area of the shaded region, Not Sufficient

(2) Angle AOR = 45° ;Angle AOR and Angle SOB or the total shaded region contribute \(\frac{1}{4}\) of the area f the circle,since 45+45=\(90^{\circ}\).But we don't know the radius of the circle to get the area. Not Sufficient

(1)+(2) area of the circle=16\(\pi\) and area of the shaded region= 16\(\pi\)/4=4\(\pi\),Sufficient

Correct Answer C
User avatar
Nunuboy1994
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 564
Own Kudos:
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 564
Kudos: 119
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the figure above, if O is the center of the circle, what is the area of the shaded region?

(1) AB = 8
(2) Angle AOR = 45°.

In order to solve this question we need to know radius length, or diameter (in which case the radius length can be derived) and we also need to know what the angle of either AOP or SOB is.

Statement (1) gives us the length of the diameter because A and B are vertexes on the circumference of the circle; therefore, we know that the radius is 8. However, we do not know the angle of either AOP or SOB- we need either angle in order to calculate the are of the shaded region because those angles are central angles ( graphically assumed). Insufficient.

Statement (2) gives us the angle of AOR which is the opposite the angle of SOB. We can plug 45 as value for X into the area of an arc formula in order to start calculating the area of both arcs; yet, we do not know the radius length. Insufficient.

Each statement, however, provides the other's missing variable- hence, we can combine statement (1) and statement (2) in order to solve the problem.
User avatar
KrishnakumarKA1
Joined: 05 Jan 2017
Last visit: 13 Oct 2020
Posts: 410
Own Kudos:
Given Kudos: 15
Location: India
Posts: 410
Kudos: 296
Kudos
Add Kudos
Bookmarks
Bookmark this Post
angle AOR = angle BOS
area of the shaded region =2*angle at the center/360 x pi x r^2

St 1: BA = 2r = 8. therefore r = 4. No idea about the angle. INSUFFICIENT

St 2: angle = 45. No idea about the r. INSUFFICIENT

St 1 & St 2: angle =45 and r=4. putting these value in the above expression, the area can be calculated.

option C
Moderator:
Math Expert
97874 posts