In the xy-plane, the vertex of a square are (1, 1), (1,-1), : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 08 Dec 2016, 05:15
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the xy-plane, the vertex of a square are (1, 1), (1,-1),

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 14 Dec 2009
Posts: 19
Followers: 0

Kudos [?]: 17 [1] , given: 3

In the xy-plane, the vertex of a square are (1, 1), (1,-1), [#permalink]

Show Tags

New post 21 Dec 2009, 02:33
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (02:29) correct 41% (01:57) wrong based on 142 sessions

HideShow timer Statistics

In the xy-plane, the vertex of a square are (1, 1), (1,-1), (-1, -1), and (-1,1). If a point falls into the square region, what is the probability that the ordinates of the point (x,y) satisfy that x^2+y^2>1?

(A) 1-pi/4
(B) pi/2
(C) 4-pi
(D) 2-pi
(E) Pi-2
[Reveal] Spoiler: OA
Intern
Intern
avatar
Joined: 13 Oct 2009
Posts: 22
Location: Hyderabad
Schools: ISB, UCLA,Darden
Followers: 0

Kudos [?]: 13 [0], given: 1

Re: probability [#permalink]

Show Tags

New post 21 Dec 2009, 03:37
1
This post was
BOOKMARKED
delta09 wrote:
In the xy-plane, the vertex of a square are (1, 1), (1,-1), (-1, -1), and (-1,1). If a point falls into the square region, what is the probability that the ordinates of the point (x,y) satisfy that x^2+y^2>1?
(A) 1-pi/4
(B) pi/2
(C) 4-pi
(D) 2-pi
(E) Pi-2

kindly help me to understand the q and provide a simple , step by step digesteble solution


\(x^2 + y^2 = R^2\) is the equation of a circle with centre (0,0) and radius R

If we draw the square and the circle, then we will see that the circle is inscribed in the square i.e. the diameter of the circle is equal to the length of the side of square.

Area of the circle= pi (1)^2=pi
Area of the square=(2)^2 = 4

The proabibility that the point lies within the square and outside the circle is

(Area of the sqaure - area of the circle)/area of the circle
= 4-pi/4
=1 - pi/4

Plz. let me know if the OA is A.

Thanks
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6853

Kudos [?]: 90044 [1] , given: 10402

In the xy-plane, the vertex of a square are (1, 1), (1,-1), [#permalink]

Show Tags

New post 21 Dec 2009, 03:40
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
delta09 wrote:
In the xy-plane, the vertex of a square are (1, 1), (1,-1), (-1, -1), and (-1,1). If a point falls into the square region, what is the probability that the ordinates of the point (x,y) satisfy that x^2+y^2>1?
(A) 1-pi/4
(B) pi/2
(C) 4-pi
(D) 2-pi
(E) Pi-2

kindly help me to understand the q and provide a simple , step by step digesteble solution


First note that the square we have is centered at the origin, has the length of the sides equal to 2 and the area equal to 4.

\(x^2+y^2=1\) is an equation of a circle also centered at the origin, with radius 1 and the \(area=\pi{r^2}=\pi\).

We are told that the point is IN the square and want to calculate the probability that it's outside the circle (\(x^+y^2>1\) means that the point is outside the given circle):
Attachment:
Untitled.png
Untitled.png [ 9.91 KiB | Viewed 1739 times ]


P=Favorable outcome/Total number of possible outcomes.

Favorable outcome is the area between the circle and the square=\(4-\pi\)
Total number of possible outcomes is the area of the square (as given that the point is in the square) =\(4\)

\(P=\frac{4-\pi}{4}=1-\frac{\pi}{4}\)

Answer: A.

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?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 4139
Followers: 306

Kudos [?]: 3249 [0], given: 100

Re: probability [#permalink]

Show Tags

New post 21 Dec 2009, 04:46
hi .. i think ans will be D...
2 is the diag and not side and each side is 2^(1/2)... area is 2...
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6853

Kudos [?]: 90044 [0], given: 10402

Re: probability [#permalink]

Show Tags

New post 21 Dec 2009, 05:05
chetan2u wrote:
hi .. i think ans will be D...
2 is the diag and not side and each side is 2^(1/2)... area is 2...


Not so.

In our case we have "horizontal" square: side=2, area=4.

We would have the square with diagonal 2 if the vertices were: (0,1), (1,0), (0,-1), (-1,0). In this case if the point is IN the square it can not be outside the circle, as the square, in this case, is inscribed in the circle. Hence the probability would be 0.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 4139
Followers: 306

Kudos [?]: 3249 [0], given: 100

Re: probability [#permalink]

Show Tags

New post 21 Dec 2009, 05:18
u r correct , i should have marked it on graph before ans .....
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

1 KUDOS received
Manager
Manager
User avatar
Joined: 25 Aug 2009
Posts: 175
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 12

Kudos [?]: 175 [1] , given: 3

Re: probability [#permalink]

Show Tags

New post 21 Dec 2009, 12:48
1
This post received
KUDOS
1-pi/4
A

Decent question. Need to have some basic knowledge of coordinate geometry for this.
_________________

Rock On

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12894
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: In the xy-plane, the vertex of a square are (1, 1), (1,-1), [#permalink]

Show Tags

New post 05 Oct 2014, 20:06
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
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12894
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: In the xy-plane, the vertex of a square are (1, 1), (1,-1), [#permalink]

Show Tags

New post 11 Oct 2015, 20:00
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

Re: In the xy-plane, the vertex of a square are (1, 1), (1,-1),   [#permalink] 11 Oct 2015, 20:00
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? MathRevolution 3 20 Aug 2016, 23:04
40 Experts publish their posts in the topic The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) amitasagar23 12 30 Dec 2013, 06:05
5 Experts publish their posts in the topic The value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) excelingmat 6 10 Oct 2015, 20:40
10 The three squares above share vertex A with AF = FE and AE = fozzzy 8 09 Jan 2013, 19:34
17 Experts publish their posts in the topic In the xy-plane, a triangle has vertexes (0,0), (4,0) and apoorvasrivastva 15 16 Nov 2009, 06:27
Display posts from previous: Sort by

In the xy-plane, the vertex of a square are (1, 1), (1,-1),

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.