Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4124

Region R is a square in the xy plane with vertices [#permalink]
Show Tags
08 Feb 2013, 11:45
5
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
Question Stats:
63% (03:52) correct
38% (02:23) wrong based on 263 sessions
HideShow timer Statistics
Region R is a square in the xy plane with vertices J = (–1, –2), K = (–1, 4), L = (5, 4), and M = (5, –2). What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? (A) \(\frac{5}{12}\) (B) \(\frac{5}{18}\) (C) \(\frac{5}{24}\) (D) \(\frac{5}{36}\) (E) \(\frac{5}{72}\)For thoughts on geometric probability, as well as a complete solution with diagram to this particular problem, see: http://magoosh.com/gmat/2013/geometric ... thegmat/Experts: are there any words of wisdom you would like to share on the topic of Geometric Probability? Mike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test Prep





Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 641
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
08 Feb 2013, 12:03
1
This post received KUDOS
mikemcgarry wrote: Region R is a square in the xy plane with vertices J = (–1, –2), K = (–1, 4), L = (5, 4), and M = (5, –2). What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? (A) \(\frac{5}{12}\) (B) \(\frac{5}{18}\) (C) \(\frac{5}{24}\) (D) \(\frac{5}{36}\) (E) \(\frac{5}{72}\)For thoughts on geometric probability, as well as a complete solution with diagram to this particular problem, see: http://magoosh.com/gmat/2013/geometric ... thegmat/Experts: are there any words of wisdom you would like to share on the topic of Geometric Probability? Mike Basically the square is formed with 4 lines x=1, x=5, y=2,y=4 Area of square =36 Now line is given as 5y=3x10 We can see that the points on which this line intersects 4 lines forming square are (0,2) and (5,1) Thus area of triangle formed under the line =15/2 Probability of a point in this area=(15/2)/36 =5/24 Ans C it is!
_________________
Lets Kudos!!! Black Friday Debrief



Manager
Joined: 08 Dec 2012
Posts: 66
Location: United Kingdom
WE: Engineering (Consulting)

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
09 Feb 2013, 18:25
1
This post received KUDOS
The square is formed by x=5 & x=1 ; y=4 & y=2
1 to 5 or 2 to 4 = 6 which is the length of the square (if it was an rectangle we would have to find the length and breadth)
So the area of the square is 36.
To find the points where the line 3x5y=10 cuts across the square, insert the two values of x or y into the equation
x=5 => 3*55y=10 => y=1. So (5,1) is first point of intersection of the line with the square.
x=1 => 3*(1)5y=10 => y=(7/5). This point (1, 7/5) is not on any of the boundary of the square so this is not relevant. Let's try inserting the values of y to find where is the second point of intersection is
y=2 => 3x5*(2)=10 => x=0. So (0, 2) is the second point of intersection of the line with the square.
So the line cuts the square at two adjacent sides of the square to form a triangle with base 5 and height 3. Area of this triangle is 15/2
Probability of point lying in this triangle = (15/2)/36 = 5/24



Manager
Joined: 06 Jun 2010
Posts: 160

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
05 Mar 2013, 11:26
1 doubt i have here is that if we try to find x intercept of that line,we get x =10/3 but as per the discussion here,the line intercepts x axis at 5,1.
Thanks, Shreeraj



Manager
Joined: 28 Jul 2011
Posts: 238

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
16 Mar 2013, 00:21
will vote for C
Area of square = 36
line passes thr' = (0,2) & (0.3.3)
Line intersect the square @ = (0,2) & (5,1)  this forms a triangle with base=5 and height = 3
Area of triangle = 15/2
probability = 15/2 * 1/36 = 5 / 24



Intern
Joined: 19 Jul 2010
Posts: 11

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
03 May 2013, 23:32
mikemcgarry wrote: Region R is a square in the xy plane with vertices J = (–1, –2), K = (–1, 4), L = (5, 4), and M = (5, –2). What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? (A) \(\frac{5}{12}\) (B) \(\frac{5}{18}\) (C) \(\frac{5}{24}\) (D) \(\frac{5}{36}\) (E) \(\frac{5}{72}\)For thoughts on geometric probability, as well as a complete solution with diagram to this particular problem, see: http://magoosh.com/gmat/2013/geometric ... thegmat/Experts: are there any words of wisdom you would like to share on the topic of Geometric Probability? Mike Hi, i might be wrong in here, please correct me. prob = area of triangle / total square area. but in the question it is What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? so shouldn't the answer be 1  (5/24) thanks in advance



MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4390
Location: India
City: Pune
GPA: 3.4
WE: Business Development (Manufacturing)

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
04 May 2013, 08:26
tarunjagtap wrote: mikemcgarry wrote: Region R is a square in the xy plane with vertices J = (–1, –2), K = (–1, 4), L = (5, 4), and M = (5, –2). What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? (A) \(\frac{5}{12}\) (B) \(\frac{5}{18}\) (C) \(\frac{5}{24}\) (D) \(\frac{5}{36}\) (E) \(\frac{5}{72}\)For thoughts on geometric probability, as well as a complete solution with diagram to this particular problem, see: http://magoosh.com/gmat/2013/geometric ... thegmat/Experts: are there any words of wisdom you would like to share on the topic of Geometric Probability? Mike Hi, i might be wrong in here, please correct me. prob = area of triangle / total square area. but in the question it is What is the probability that a randomly selected point in region R lies below the line 3x – 5y = 10? so shouldn't the answer be 1  (5/24) thanks in advance Hi Tarun, Go thru the attached figure. then you will come to know what are you missing exactly. Narenn
Attachments
cord prob.png [ 22.27 KiB  Viewed 3525 times ]
_________________
Every Wednesday: Meet MBA Experts in Chat Room and Ask Your MostPressing MBA Admission Questions to them in a Live Chat.
Must Read Forum Topics Before You Kick Off Your MBA Application
New GMAT Club Decision Tracker  Real Time Decision Updates



Intern
Joined: 19 Jul 2010
Posts: 11

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
04 May 2013, 08:47
Narenn wrote: Hi Tarun,
Go thru the attached figure. then you will come to know what are you missing exactly.
Narenn
oh ok .. got it.. thanks Narenn.. I dont know what was going through my mind.. actually i plotted the line wrongly.. hence the stupid question.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
22 Aug 2014, 15:42
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: 15918

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
08 Dec 2015, 10:44
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



Intern
Joined: 28 Dec 2015
Posts: 42

Re: Region R is a square in the xy plane with vertices [#permalink]
Show Tags
12 Jul 2016, 03:46
X=5 is the equation of the line LM 3x5y=10 intersects y axis at 2 and x=5 at (5,1).
So,we get a triangle whose area=1/2*5*3=15/2 Now Area of square=6^2=36
So,probability=15/2/36=15/72=5/24




Re: Region R is a square in the xy plane with vertices
[#permalink]
12 Jul 2016, 03:46








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


4


In the coordinate plane, one of the vertices of a square is the point

Bunuel 
4 
17 Jun 2017, 02:36 

17


Three of the four vertices of a rectangle in the xycoordinate plane

Bunuel 
12 
15 Oct 2016, 21:18 

3


In the xy plane, the square region bound by (0,0), (10, 0)

mikemcgarry 
20 
14 Sep 2014, 07:20 

71


In the coordinate plane, rectangular region R has vertices a

shrive555 
17 
18 Nov 2016, 05:26 

9


In the xy plane, the vertices of a triangle have coordinates

monirjewel 
10 
14 Nov 2016, 07:09 



