May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 229
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)

What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
Updated on: 18 Feb 2018, 11:46
Question Stats:
63% (01:49) correct 37% (01:58) wrong based on 351 sessions
HideShow timer Statistics
m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ? A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
KUDOS is the good manner to help the entire community.
"If you don't change your life, your life will change you"
Originally posted by Rock750 on 06 Apr 2013, 11:17.
Last edited by Bunuel on 18 Feb 2018, 11:46, edited 2 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 55271

What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
07 Apr 2013, 04:38
m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) The circle represented by the equation \(x^2+y^2 = 4\) is centered at the origin and has the radius of \(r=\sqrt{4}=2\). Look at the diagram below: We need to find the area of the upper crescent, so the area of the yellow sector. Since the central angle of this sector is 90 degrees then its area would be 1/4 of that of the circle (since circle is 360 degrees). The area of the circle is \({\pi}{r^2}=4\pi\), 1/4 of this value is \(\pi\). Answer: D. Attachment:
m2220.png [ 16.59 KiB  Viewed 7360 times ]
_________________




VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1051
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
06 Apr 2013, 11:58
Rock750 wrote: What is the area of the region enclosed by lines y=x, x=−y, and the upper crescent of the circle y^2+x^2=4 ?
A \(Pi/4\)
B \(Pi/2\)
C \(3Pi/4\)
D \(Pi\)
E \(4Pi\) \(y^2+x^2=4\) is a circle with its center in the origin (0,0) The lines \(y=x\) and \(y=x\) intersect in (0,0) and form an angle of 90° between them. The area of the circle is \(r^2PI=4PI\), now we are looking for "area of the region enclosed by lines y=x, x=−y, and the upper crescent of the circle y^2+x^2=4", which can be found through this equation \(4PI : 360=x : 90\) (Tot area : Tot angle = x : angBetweenLines) D \(x=PI\)
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Senior Manager
Joined: 16 Dec 2011
Posts: 296

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
06 Apr 2013, 20:56
The lines y=x, x=−y intersecting at (0,0) and they are perpendicular to each other. The circle y^2+x^2=4 is centered at (0,0) and has a radius of 2. These two lines are dividing the circle y^2+x^2=4 into four equal segments. Area of each segment = (PI*r^2) / 4 = (PI*2^2) / 4 = PI
Answer is D.



Intern
Joined: 26 Jan 2013
Posts: 11

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
08 Apr 2013, 12:45
Hi Bunuel, in the above problem, i understand that the circle is centered at the origin and has radius 2 but lines y=x, and x = 1 represents the half of the circle so the area enclosed should be half of the total area, I mean 4pi/2. i know, i am missing something, please clarify! and How do I know that question asks the area of upper 1/4 of the area or How do i determine the 90 degree portion??



Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 151
GMAT 1: 530 Q43 V20 GMAT 2: 560 Q42 V25 GMAT 3: 650 Q48 V31

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
08 Apr 2013, 13:01
kamalahmmad1 Quote: How do i determine the 90 degree portion Two lines are perpendicular if their slopes are ve reciprocal of each other. E.g. line 1 : y = mx and line 2: y = (1/m)x then line 1 and line two are perpendicular Here y = x and y = x meet the above stated criteria for perpendicular lines //kudos please, if the above explanation is good.
_________________
KUDOS is a way to say Thank You



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
09 Apr 2013, 03:46
kamalahmmad1 wrote: Hi Bunuel, in the above problem, i understand that the circle is centered at the origin and has radius 2 but lines y=x, and x = 1 represents the half of the circle so the area enclosed should be half of the total area, I mean 4pi/2. i know, i am missing something, please clarify! and How do I know that question asks the area of upper 1/4 of the area or How do i determine the 90 degree portion?? The two lines are y=x and y=x (x=y), not x = 1. Both lines are shown on the diagram in my post. Lines y=x and y=x make 90 degrees.
_________________



Intern
Joined: 03 Apr 2012
Posts: 23

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
11 Aug 2013, 10:18
To find the Area of a sector
Arc angle Area of sector ___________ = ______________ 360 Area of circle
90 Area of sector ___ = _____________ 360 4 Pi
Area of sector = 4 pi x 90/ 360 = pi



Senior Manager
Joined: 10 Jul 2013
Posts: 312

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
13 Aug 2013, 15:26
Rock750 wrote: m22 q20
What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?
A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) ... My solution(with detail explanation): This diagram is indispensable:
Attachments
line and circle.png [ 42.47 KiB  Viewed 6539 times ]
_________________



Manager
Status: Applied
Joined: 02 May 2014
Posts: 126
Location: India
Concentration: Operations, General Management
Schools: Tulane '18 (A), Tippie '18 (D), Moore '18, Katz '18 (D), UCSD '18, Madison '18, Olin '18 (S), Simon '18, Desautels '18 (I), Sauder '18 (S), Terry '18 (WL), GWU '18, Neeley '18 (WL), Weatherhead '18 (S), Fox(Temple)'18, Eller FT'18 (A), Schulich Sept"18 (S)
GPA: 3.35
WE: Information Technology (Computer Software)

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
19 Dec 2014, 04:53
All the 3 parts i.e x=y; x=y; and x^2+y^2=4 makes one forth of the circular region x^2+y^2=4 area of which is 4pi so the required area is pi. hope this one makes it clear.



Intern
Joined: 30 May 2014
Posts: 15
WE: Information Technology (Consulting)

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
10 Oct 2015, 02:36
sajib2126 wrote: What is the area of the region enclosed by lines y=x, x=−y, and the upper crescent of the circle y^2+x^2=4 ? a.π/4 b. π/2 c. π/4 d. π e.4π Question corrected! Circle is y^2+x^2=4 has radius 2. Area of circle = pi * 4 y=x is the line that passes through 1 and 3 quadrants which has 45 degree to xaxis. y=x is the line that passes through 2 and 4 quadrants which has 45 degree to xaxis. The two lines, divides the circle into 4 parts. Combining all the three, (question to find the area of the upper crescent) Area = 4 pi/4 = pi



Intern
Joined: 26 Jul 2014
Posts: 12

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
10 Oct 2015, 02:42
Why or How does Circle is y^2+x^2=4 has radius 2 ?



Intern
Joined: 30 May 2014
Posts: 15
WE: Information Technology (Consulting)

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
10 Oct 2015, 02:58
sajib2126 wrote: Why or How does Circle is y^2+x^2=4 has radius 2 ? In the equation x^2+y^2=4 all the points (2,2)(2,2)(0,2)(2,0) are on the circle. And these have the center as (0,0) Hence the radius is 2. Another explanation:Equation Of A Circle (x  a)^2 + (y  b)^2 = r^2 where a is the x coordinate of the centre of the circle b is the y coordinate of the centre of the circle r is the radius of the circle Comparing the above equation with the equation (x0)^2+(y0)^2=4 r^2 = 4 r=2 center is (0,0)



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 275

What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
19 Feb 2018, 15:36
sajib2126 wrote: Why or How does Circle is y^2+x^2=4 has radius 2 ? hi the area of the circle is represented by the equation, x^2 + y^2 = 4, means that the area of the circle is x^2 + y^2 = 4 now, as 2 sides are equal to each other, it can be said that area is (x^2 + y^2) OR 4 since area is 4, the radius is 2 I don't know whether this reasoning is okay, but I have seen the scenario this way Expert's reply on this issue is highly desired thanks ???



Manager
Joined: 27 Jul 2017
Posts: 50

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
20 Feb 2018, 20:33
Bunuel wrote: m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) The circle represented by the equation \(x^2+y^2 = 4\) is centered at the origin and has the radius of \(r=\sqrt{4}=2\). Look at the diagram below: Attachment: m2220.png We need to find the area of the upper crescent, so the area of the yellow sector. Since the central angle of this sector is 90 degrees then its area would be 1/4 of that of the circle (since circle is 360 degrees). The area of the circle is \({\pi}{r^2}=4\pi\), 1/4 of this value is \(\pi\). Answer: D. Hi Bunuel, I was able to solve this question but it took me a while to visualise the diagram. So just asking by curiosity, can we expect this type of questions in GMAT? As always appreciate your efforts in advance! Thanks
_________________
Ujjwal Sharing is Gaining!



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
20 Feb 2018, 20:47
ujjwal80 wrote: Bunuel wrote: m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) The circle represented by the equation \(x^2+y^2 = 4\) is centered at the origin and has the radius of \(r=\sqrt{4}=2\). Look at the diagram below: Attachment: m2220.png We need to find the area of the upper crescent, so the area of the yellow sector. Since the central angle of this sector is 90 degrees then its area would be 1/4 of that of the circle (since circle is 360 degrees). The area of the circle is \({\pi}{r^2}=4\pi\), 1/4 of this value is \(\pi\). Answer: D. Hi Bunuel, I was able to solve this question but it took me a while to visualise the diagram. So just asking by curiosity, can we expect this type of questions in GMAT? As always appreciate your efforts in advance! Thanks Yes, I think it's a perfectly valid question. Notice that the average time it took users to answer it correctly is just 1:07 minutes.
_________________



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 275

What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
24 Feb 2018, 07:19
ujjwal80 wrote: Bunuel wrote: m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) The circle represented by the equation \(x^2+y^2 = 4\) is centered at the origin and has the radius of \(r=\sqrt{4}=2\). Look at the diagram below: Attachment: m2220.png We need to find the area of the upper crescent, so the area of the yellow sector. Since the central angle of this sector is 90 degrees then its area would be 1/4 of that of the circle (since circle is 360 degrees). The area of the circle is \({\pi}{r^2}=4\pi\), 1/4 of this value is \(\pi\). Answer: D. Hi Bunuel, I was able to solve this question but it took me a while to visualise the diagram. So just asking by curiosity, can we expect this type of questions in GMAT? As always appreciate your efforts in advance! Thanks hi as far as time is concerned, you can see the problem this way (y =x), means slope is 1 and the line passes through the origin (y = x), means slope is 1, and the line passes through the origin now it is worth noticing that a slope of 1 or 1 creates an angle of 45 degree, so 2 slopes jointly cover a 90 degree also, when 2 lines are perpendicular to each other, their slopes are negative reciprocal to each other here 1 is negative reciprocal to 1, so the slopes are perpendicular to each other, creating an angle 90 degree thus, 2 slopes together add to 90 degrees, which is 1/4 of pi (2)^2 , as the radius is 2 we get from (x^ + Y^ = 4) OR you can simply draw the 2 slopes to see the area covered by the upper crescent hope this helps and is clear! thanks and cheers!



Manager
Joined: 27 Jul 2017
Posts: 50

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
24 Feb 2018, 20:01
gmatcracker2018 wrote: ujjwal80 wrote: Bunuel wrote: m22 q20What is the area of the region enclosed by lines \(y=x\), \(x=y\), and the upper crescent of the circle \(y^2+x^2=4\) ?A. \(\frac{\pi}{4}\) B. \(\frac{\pi}{2}\) C. \(\frac{3\pi}{4}\) D. \(\pi\) E. \(4\pi\) The circle represented by the equation \(x^2+y^2 = 4\) is centered at the origin and has the radius of \(r=\sqrt{4}=2\). Look at the diagram below: Attachment: m2220.png We need to find the area of the upper crescent, so the area of the yellow sector. Since the central angle of this sector is 90 degrees then its area would be 1/4 of that of the circle (since circle is 360 degrees). The area of the circle is \({\pi}{r^2}=4\pi\), 1/4 of this value is \(\pi\). Answer: D. Hi Bunuel, I was able to solve this question but it took me a while to visualise the diagram. So just asking by curiosity, can we expect this type of questions in GMAT? As always appreciate your efforts in advance! Thanks hi as far as time is concerned, you can see the problem this way (y =x), means slope is 1 and the line passes through the origin (y = x), means slope is 1, and the line passes through the origin now it is worth noticing that a slope of 1 or 1 creates an angle of 45 degree, so 2 slopes jointly cover a 90 degree also, when 2 lines are perpendicular to each other, their slopes are negative reciprocal to each other here 1 is negative reciprocal to 1, so the slopes are perpendicular to each other, creating an angle 90 degree thus, 2 slopes together add to 90 degrees, which is 1/4 of pi (2)^2 , as the radius is 2 we get from (x^ + Y^ = 4) OR you can simply draw the 2 slopes to see the area covered by the upper crescent hope this helps and is clear! thanks and cheers! Thanks, gmatcracker2018, I will keep your explanation in mind next time I see such question.
_________________
Ujjwal Sharing is Gaining!



NonHuman User
Joined: 09 Sep 2013
Posts: 11012

Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
Show Tags
09 Mar 2019, 02:55
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.
_________________




Re: What is the area of the region enclosed by lines y=x, x=−y,
[#permalink]
09 Mar 2019, 02:55






