Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 18 Jun 2010
Posts: 300
Schools: Chicago Booth Class of 2013

In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
20 Aug 2010, 14:30
5
This post received KUDOS
28
This post was BOOKMARKED
Question Stats:
68% (04:10) correct
32% (02:48) wrong based on 299 sessions
HideShow timer Statistics
In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant? A. \(\frac{\pi}{\pi+\sqrt{2}}\) B. \(\frac{\pi}{\pi+1}\) C. \(\sqrt{\frac{2}{\pi}}\) D. \(\frac{\pi+2}{2\pi}\) E. \(\frac{2\pi}{2\pi+1}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 19 Apr 2012, 11:53, edited 1 time in total.
Edited the question, added the answer choices and OA



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 685
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
20 Aug 2010, 14:48
1
This post received KUDOS
Ok so I am typing this on my mobile with imagination... Imagine a square of side 1 and a circle circumscribed.. Qn is what is the area that is lying on the 2 bulging sides.. Area of square = 1 area of circle = pi/2 The area of 4 bulging sides = (pi/21) Fraction of circle area inside 1st Q= [pi/21/2(pi/21)]/pi/2 = (pi/2pi/4+1/2)/(pi/2) = (pi/4+1/2)/(pi/2) = (pi+2)/2pi Posted from my mobile device
_________________
Consider kudos, they are good for health
Last edited by mainhoon on 20 Aug 2010, 16:05, edited 2 times in total.



Math Expert
Joined: 02 Sep 2009
Posts: 39642

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
20 Aug 2010, 15:15
5
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
Financier wrote: In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?
Answerchoises will come later. Look a the diagram: Attachment:
CS.jpg [ 22.42 KiB  Viewed 9174 times ]
We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be xaxis and left side of square to be yaxis. We need to find the ratio of area of a circle without the red parts to the area of whole circle. Area of a circle is \(C=\pi{r^2}=\pi\); Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\); Ratio of the are of this region to area of a circle is \(\frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}\). Answer: D. Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Apr 2010
Posts: 30

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
23 Oct 2010, 13:33
Let us assume A to be (1,1).Then, distance from origin = sqrt 2 = Diagonal of square = Diameter of circle.
Area of square = 1 sq units and Area of circle = Pi r^2 = Pi (sqrt 2 / 2)^2 = Pi / 2
Area of 4 bulging sides = (Pi/2)  1 = (Pi  2) / 2 and Area of 2 bulging side = (Pi  2) / 4.
Therefore, required fraction = Area of 2 bulging side / Area of circle = [(Pi  2) / 4] / (Pi/2) = Pi 2 / 2Pi.
But answer posted by Bunuel is : Pi + 2 / 2Pi and I take his explainations as absolute. Since I got a different answer....please explain where I am wrong.



Senior Manager
Joined: 10 Nov 2010
Posts: 262
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
19 Apr 2012, 11:44
Area of circle = pie(r^2) diagonal of square = 2^1/2*side 2^1/2*side = 2r side = r*2^1/2 area of square = 2(r^2) Area of red portion = Area of Circle  Area of square /2 = pie2/2pie Pls correct me if wrong
_________________
The proof of understanding is the ability to explain it.



Math Expert
Joined: 02 Sep 2009
Posts: 39642

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
19 Apr 2012, 12:00



Manager
Status: Married
Joined: 30 Oct 2010
Posts: 64
Location: India
Concentration: Marketing, Finance
GPA: 2.9
WE: Information Technology (Computer Software)

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
19 Apr 2012, 22:08
mainhoon wrote: Ok so I am typing this on my mobile with imagination... Imagine a square of side 1 and a circle circumscribed.. Qn is what is the area that is lying on the 2 bulging sides.. Area of square = 1 area of circle = pi/2
The area of 4 bulging sides = (pi/21) Fraction of circle area inside 1st Q= [pi/21/2(pi/21)]/pi/2 = (pi/2pi/4+1/2)/(pi/2) = (pi/4+1/2)/(pi/2) = (pi+2)/2pi
Posted from my mobile device Great work!!...Appreciate the stratgy.
_________________
KUDOSing does'nt cost you anything, but might just make someone's day!!!
"Musings of a Muddled Muggle Mind" http://felinesmile.blogspot.in/ ...comments Welcome



Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 259
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
08 Aug 2012, 08:57
Hi, Cant we do this by calculating the area of the sector and then the area of the circle??? Pls help me understand!
_________________
I've failed over and over and over again in my life and that is why I succeedMichael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+



Senior Manager
Joined: 15 Jun 2010
Posts: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
08 Aug 2012, 17:41
es we can do it by taking any value for (d,d) and calculating the area deducting the sector. Take (d,d) as 2,2. the dia meter becomes 2 root 2 and radius root2 so area of circle = 2pie area of 2 sectors= 2*(90/360)*2 pie = pie But have to add another half of square = 1/2 * 4 = 2 So area in 1st quadrant = 2piepie+2= pie+2 and area of circle = 2pie So ratio= (2+pie)/2pie
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html



Manager
Status: K... M. G...
Joined: 22 Oct 2012
Posts: 51
Concentration: General Management, Leadership
GMAT Date: 08272013
GPA: 3.8

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
23 Jan 2013, 10:15
Bunuel wrote: Financier wrote: In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?
Answerchoises will come later. Look a the diagram: Attachment: CS.jpg We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be xaxis and left side of square to be yaxis. We need to find the ratio of area of a circle without the red parts to the area of whole circle. Area of a circle is \(C=\pi{r^2}=\pi\); Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\); Ratio of the are of this region to area of a circle is \(\frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}\). Answer: D. Hope it's clear. Hi, Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\);is already describing the circle's portion, which is available in 1st Q. why we have again check for the ratio b/w this and circle again.I got this doubt since question has asked us to find the fraction of the area of circle C lies within the first quadrant. Kindly help me understand ..



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
23 Jan 2013, 14:19
1
This post was BOOKMARKED
FTG wrote: Bunuel wrote: Financier wrote: In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?
Answerchoises will come later. Look a the diagram: Attachment: CS.jpg We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be xaxis and left side of square to be yaxis. We need to find the ratio of area of a circle without the red parts to the area of whole circle. Area of a circle is \(C=\pi{r^2}=\pi\); Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\); Ratio of the are of this region to area of a circle is \(\frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}\). Answer: D. Hope it's clear. Hi, Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\);is already describing the circle's portion, which is available in 1st Q. why we have again check for the ratio b/w this and circle again.I got this doubt since question has asked us to find the fraction of the area of circle C lies within the first quadrant. Kindly help me understand .. The question asks for "fraction" or "proportion" of the circle. (e.g. say 1/2 or 3/5th of circle lies in the first quadrant) Hence you need to take the ratio of Area (in 1st quadrant) to Total area to find the fraction.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Intern
Joined: 03 Jan 2013
Posts: 15

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
04 Feb 2013, 09:37
Bunuel wrote: Financier wrote: In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?
Answerchoises will come later. Look a the diagram: Attachment: CS.jpg We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be xaxis and left side of square to be yaxis. We need to find the ratio of area of a circle without the red parts to the area of whole circle. Area of a circle is \(C=\pi{r^2}=\pi\); Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\); Ratio of the are of this region to area of a circle is \(\frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}\). Answer: D. Hope it's clear. Quote: Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); is this because you are taking into account the portion of the square which doesnt touch the red parts of the circle? Since area of Square is A = a^2 ?



Math Expert
Joined: 02 Sep 2009
Posts: 39642

Re: What fraction of the area of circle C lies within ... [#permalink]
Show Tags
05 Feb 2013, 03:40
pharm wrote: Bunuel wrote: Financier wrote: In a rectangular coordinate system, point A has coordinates (d, d), where d > 0. Point A and the origin form the endpoints of a diameter of circle C. What fraction of the area of circle C lies within the first quadrant?
Answerchoises will come later. Look a the diagram: Attachment: CS.jpg We have circle with radius=1 and square inscribed in it. Now imagine the base of square to be xaxis and left side of square to be yaxis. We need to find the ratio of area of a circle without the red parts to the area of whole circle. Area of a circle is \(C=\pi{r^2}=\pi\); Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); Area of a circle without the red parts is \(C\frac{CS}{2}=\pi\frac{\pi2}{2}=\frac{\pi+2}{2}\); Ratio of the are of this region to area of a circle is \(\frac{\frac{\pi+2}{2}}{\pi}=\frac{\pi+2}{2\pi}\). Answer: D. Hope it's clear. Quote: Area of a square is half of the product of diagonals, as diagonal equals to \(2r=2\), then \(S=\frac{2^2}{2}=2\); is this because you are taking into account the portion of the square which doesnt touch the red parts of the circle? Since area of Square is A = a^2 ? If I understand correctly you are asking about the area of a square: \(area_{square}=side^2=\frac{diagonal^2}{2}\). This is a general formula for the area of any square. Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 03 Jan 2013
Posts: 15

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
05 Feb 2013, 05:50
Yea, thank you cleared things up



Math Expert
Joined: 02 Sep 2009
Posts: 39642

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
05 Feb 2013, 05:55



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15942

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
22 Aug 2014, 15:54
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15942

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
06 Dec 2015, 03:08
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 05 Sep 2014
Posts: 90

In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
19 Aug 2016, 13:10
why we are considering square for this question, its nowhere specified in the question. I do not get this at all, please help.
Regards Megha



Intern
Joined: 29 Mar 2015
Posts: 12

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
19 Aug 2016, 23:59
2
This post received KUDOS
1
This post was BOOKMARKED
A quick look at the answer choices tells you that the ratio does not depend on the value of "d". Hence you can choose "smart numbers" for d  For example 2. Which makes the radius of the circle sqrt(2). The all we need to do is add the area of the semi circle with the area of the triangle to get the area in the first quadrant (refer the diagram by Bunuel).
Solve and the answer is D.



Intern
Joined: 29 Mar 2015
Posts: 12

Re: In a rectangular coordinate system, point A has coordinates [#permalink]
Show Tags
20 Aug 2016, 00:11
2
This post received KUDOS
1
This post was BOOKMARKED
megha_2709 wrote: why we are considering square for this question, its nowhere specified in the question. I do not get this at all, please help.
Regards Megha If you drop perpendiculars to x & y axes from (d,d) you will get (d,0) and (0,d). These two points are "d" units away from the origin as well as from (d,d). Knowing that all sides are of the same length and that the 3 angles are 90 degrees, (we drew perpendiculars to the axes and the axes themselves are at a () degree angle) we can conclude that the figure is a square. Hope it helps.




Re: In a rectangular coordinate system, point A has coordinates
[#permalink]
20 Aug 2016, 00:11







