GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jan 2019, 20:17

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.

# In the figure above, what is the area of the shaded region?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52108
In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

17 Aug 2016, 00:50
1
00:00

Difficulty:

25% (medium)

Question Stats:

81% (00:58) correct 19% (01:05) wrong based on 101 sessions

### HideShow timer Statistics

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 [ 6 KiB | Viewed 2634 times ]

_________________
Retired Moderator
Joined: 26 Nov 2012
Posts: 591
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

17 Aug 2016, 01:04
Bunuel wrote:

In the figure above, what is the area of the shaded region?

(1) AB = 8
(2) Angle AOR = 45°.

Attachment:
2016-08-17_1248.png

To know the area of a sector we use = angle/360 ( area of circle)

Stat 1: We don't know the angle

Stat 2: We don't have radius value

Stat 1+ Stat 2: we have radius = 4 and angle 45 degrees..sufficient...

IMO option C is correct answer..

OA please...will correct if I missed anything..
Intern
Joined: 20 Dec 2014
Posts: 30
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

17 Aug 2016, 12:27
It might be wrong, but...do we know that O is the center to conclude that OA=OB ?
Manager
Joined: 15 Mar 2015
Posts: 111
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

17 Aug 2016, 13:34
I Agree with the previous post. We do not know if O is the center and can thus not solve for the area.

Posted from my mobile device
_________________

I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.

Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

17 Aug 2016, 21:15
Stn wrote:
It might be wrong, but...do we know that O is the center to conclude that OA=OB ?

Edited to make that clear.
_________________
Manager
Joined: 15 Mar 2015
Posts: 111
In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

18 Aug 2016, 00:54
Bunuel wrote:
Stn wrote:
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.

edit:
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?
_________________

I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 535
GPA: 2.81
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

18 Aug 2016, 02:16
1
Top Contributor
Bunuel wrote:

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

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Director
Joined: 12 Nov 2016
Posts: 731
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

14 Mar 2017, 15:37
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.
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 530
Location: India
Re: In the figure above, what is the area of the shaded region?  [#permalink]

### Show Tags

15 Mar 2017, 01:51
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
_________________

GMAT Mentors

Re: In the figure above, what is the area of the shaded region? &nbs [#permalink] 15 Mar 2017, 01:51
Display posts from previous: Sort by