December 14, 2018 December 14, 2018 10:00 PM PST 11:00 PM PST Carolyn and Brett  nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session. December 15, 2018 December 15, 2018 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51215

The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
22 Jul 2015, 01:04
Question Stats:
52% (02:31) correct 48% (02:05) wrong based on 238 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Aug 2009
Posts: 7106

The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
22 Jul 2015, 06:42
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. Hi, the simplest way to solve the Q here is as follows... 1)we know there are four sets of integers on the circumference... so the numerator is 4.. now we should have the denominator in the form 4X +1... only 29 fits in so ans 4/29.. although 9 is there but it will become 18 when num is 4.. WHY 4X+1?we know there are four quadrants, and there will be total 4x sets where x is total numbers in one Quad AND ADD TO IT THE SINGLE ORIGIN (0,0)ans A.. 2)if the choices are not so obvious .. 0,0 1 0,12 0,24 0,34 1,02 1,14 1,24 2,14 2,24 total 4*7+1=29 ans A
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
22 Jul 2015, 03:27
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. The standard equation of circle with center (a,b) and radius = r is \((xa)^2+(yb)^2=r^2\) For a circle at the center, (a,b) = (0,0), radius = 3 Thus the equation becomes , \(x^2+y^2 = 9\) Now all the possible points (all integers only) inside and on the circumference (in red) are [a quick trick to see what points will lie inside the circle will be to find points (x,y) that will satisfy the relation \(x^2+y^2<9\), and for points on circumference (x,y) will satisfy \(x^2+y^2=9\)] : (0,0) (1,0) (2,0) (3,0)(1,0) (2,0) (3,0)(0,1) (0,2) (0,1) (0,2) (0,3) (0,3)(2,1) (2,2) (2,1) (2,2) (1,1) (1,2) (1,1) (1,2) (2,1) (2,2) (2,1) (2,2) (1,1) (1,2) (1,1) (1,2) Thus we see , total points = 29, on circumference = 4 Thus the probability = 4/29. A is the correct answer.



Manager
Joined: 26 Dec 2011
Posts: 114

The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
22 Jul 2015, 05:59
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. Solution  Circle O with center at the origin and radius 3. Since x and y are integers, the circle touches the x and y axes at four points (3, 0), (0, 3), (3, 0) and (0, 3). Number of points inside circle O in the first quadrant are (1, 1), (1, 2), (2, 1) and (2, 2). Using symmetry, each of the 4 quadrants has 4 points. So there are 4 × 4 = 16 points inside the quadrants. Now look at the axes. The xaxis has the 7 points (3, 0), (2, 0), (1, 0), (0, 0), (1, 0), (2, 0), (3, 0). The yaxis also has 7 points. But both axes have counted the origin, so the sum is one less. So there are 7 + 7  1 = 13 points on the axes. The total number of points inside and on the circle is 16 + 13 = 29. From the graph attached, there are 4 points on the circumference of the circle. So the probability is 4/29.
Attachments
Probability.gif [ 5.74 KiB  Viewed 3939 times ]
_________________
Thanks, Kudos Please



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
22 Jul 2015, 06:17
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. 1) We don't necessarily have to find out all points in all Quadrants. No. of Points in Every Quadrant will be same so we need to calculate only the No. of points in one quadrant and multiply it by 4
2) There are 4 Axes(+X and +Y and we must take one axes with one quadrant
3) The point at the origin must be considered separately at the end as Origin involves all quadrantsAnswer Option A
Attachments
File comment: www.GMATinsight.com
Sol 1.jpg [ 155.31 KiB  Viewed 3924 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 51215

Re: The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
26 Jul 2015, 10:54
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. 800score Official Solution:Graph circle O with center at the origin and radius 3. The circle touches the x. and y axes at the four points (3, 0), (0, 3), (3, 0) and (0, 3). Since x and y are integers, it is easy to see and count the number of points inside circle O. In the first quadrant, the points are (1, 1), (1, 2), (2, 1) and (2, 2). Using symmetry, each of the 4 quadrants has 4 points. So there are 4 × 4 = 16 points inside the quadrants. Now look at the axes. The xaxis has the 7 points (3, 0), (2, 0), (1, 0), (0, 0), (1, 0), (2, 0), (3, 0). The yaxis also has 7 points. But both axes have counted the origin, so the sum is one less. So there are 7 + 7  1 = 13 points on the axes. The total number of points inside and on the circle is 16 + 13 = 29. From the graph, there are 4 points on the circumference of the circle. So the probability is 4/29.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Director
Joined: 13 Mar 2017
Posts: 666
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
13 Aug 2017, 21:49
Bunuel wrote: The set P contains the points (x, y) on the coordinate plane that are in or on circle O. The values of x and y are integers. Circle O is centered at the origin and has a radius of 3. If a point from set P is randomly selected, what is the probability that the point is located on the circumference of circle O?
A. 4/29 B. 4/28 C. 4/27 D. 4/19 E. 2/9
Kudos for a correct solution. At the first instance it looks a very complex or calculation intensive problem. But if we solve some of the similar problems we will easily understand how to tackle such problems easily. Well lets start with the coordinates which lies on the circle and we know that these points are (0,3), (3,0),(0,3),(3,0) (Just check points anticlockwise though its not mandatory.. ) Now lets start finding all the integer coordinates either inside the circle or on the circle. We will first check points in the first quadrant which doesn't lie on the x axis or y axis as the points on a&y axes are common to all quadrants. So, in the first quadrant points are (1,1)(1,2)(2,1)(2,2) ... Total 4 So, No. of points which has integral coordinates and lies within/on the circle and does not lie on x or y axis = 4*4 = 16 Now lets start finding all the integer coordinates on the positive x axis excluding origin Such point are (1,0)(2,0), (3,0) .. Total 3 So, No. of points which has integral coordinates and lies within/on the circle and lie on x or y axis (excluding origin)= 3*4 = 12 Origin ..... Total 1 So, Total no. of points which has integral coordinates and lies within/on the circle = 16+12+1 = 29 probability = 4/29 Answer A..This may be represented by a diagram also as provided by many users above.. You can refer the same... Thanks
_________________
CAT 2017 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



NonHuman User
Joined: 09 Sep 2013
Posts: 9162

Re: The set P contains the points (x, y) on the coordinate plane that are
[#permalink]
Show Tags
06 Oct 2018, 22:26
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: The set P contains the points (x, y) on the coordinate plane that are &nbs
[#permalink]
06 Oct 2018, 22:26






