Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Sep 2013
Posts: 25
Location: India
Concentration: Accounting, Finance
GMAT Date: 10252013
GPA: 3.66

Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
Updated on: 27 Sep 2013, 01:35
Question Stats:
50% (02:08) correct 50% (03:21) wrong based on 80 sessions
HideShow timer Statistics
Point P(a,b) is randomly selected in the region enclosed by the following lines: 3y + 2x = 6, x=0 and y = 0. What is the probability that b>a ? I don't have OA for this question... Can someone please explain me how to calculate the probability?
_________________
Strive for Excellence....!!!!!
Originally posted by jellybean23 on 26 Sep 2013, 23:51.
Last edited by Bunuel on 27 Sep 2013, 01:35, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 49968

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
27 Sep 2013, 01:57
KK23 wrote: Point P(a,b) is randomly selected in the region enclosed by the following lines: 3y + 2x = 6, x=0 and y = 0. What is the probability that b>a ?
I don't have OA for this question...
Can someone please explain me how to calculate the probability? Refer to the diagram below: Attachment:
Probability.png [ 13.38 KiB  Viewed 10060 times ]
The area of the triangle enclosed by 3y + 2x = 6 (y=22/3*x), x=0 and y = 0 is 1/2*2*3=3. We need the ycoordinate of P to be greater than its xcoordinate (y>x), so point P must be above line y=x and in the enclosed region. The probability of that is (favorable)/(total)=(yellow triangle)/(entire triangle). Now, we need to find intersection point of y=x and 3y+2x=6, which is (6/5, 6/5). Thus the area of yellow triangle is 1/2*6/5*2=6/5. P=(6/5)/3=2/5. Similar questions to practice: settconsistsofallpointsxysuchthatx2y21if15626.htmlinthecoordinateplanerectangularregionrhasverticesa104869.htmlinthexyplaneatrianglehasvertexes0040and86926.htmlinthexyplaneatrianglehasvertexes0040and88395.htmlHope it helps.
_________________
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




Senior Manager
Joined: 08 Apr 2012
Posts: 376

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
20 Jul 2014, 10:12
Hi Bunuel, Can you explain how you calculated the area of the triangle?



Math Expert
Joined: 02 Sep 2009
Posts: 49968

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
20 Jul 2014, 11:33



Intern
Joined: 05 May 2016
Posts: 36

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
31 Jul 2016, 04:10
Bunuel wrote: Point P(a,b) is randomly selected in the region enclosed by the following lines: 3y + 2x = 6, x=0 and y = 0. What is the probability that b>a ? I don't have OA for this question... Can someone please explain me how to calculate the probability? Refer to the diagram below: Attachment: Probability.png The area of the triangle enclosed by 3y + 2x = 6 (y=22/3*x), x=0 and y = 0 is 1/2*2*3=3. We need the ycoordinate of P to be greater than its xcoordinate (y>x), so point P must be above line y=x and in the enclosed region. The probability of that is (favorable)/(total)=(yellow triangle)/(entire triangle). Now, we need to find intersection point of y=x and 3y+2x=6, which is (6/5, 6/5). Thus the area of yellow triangle is 1/2*6/5*2=6/5. P=(6/5)/3=2/5. Similar questions to practice: settconsistsofallpointsxysuchthatx2y21if15626.htmlinthecoordinateplanerectangularregionrhasverticesa104869.htmlinthexyplaneatrianglehasvertexes0040and86926.htmlinthexyplaneatrianglehasvertexes0040and88395.htmlHope it helps. Quote: Bunuel Sir, two questions here,
Why are you considering "y=x" line. How did you get 6/5?
Please elaborate. Thanks in advance.



Intern
Joined: 08 Oct 2016
Posts: 22
Location: Nepal
Concentration: Finance, Marketing
WE: Account Management (Accounting)

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
27 Jan 2017, 02:27
how do we get this point of intersection?



Manager
Joined: 24 Dec 2016
Posts: 92
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
23 Feb 2017, 22:52
GovindAgrawal wrote: how do we get this point of intersection? Hi, Let me try explaining. It took me a while figuring it out myself. First, we can replace the lines x=0 and y=0 by a line x=y. That leaves us with just 2 lines : 1st is x=y and 2nd is 3y= 2x + 6. To find the intersection of these 2 lines, equate the RHS variables and you'll get x=6/5. [ 2x+6 = x ]Now, substitute the value of x in either of the 2 equations and you'll get the y coordinate for the point. Does that help ?



CEO
Joined: 08 Jul 2010
Posts: 2537
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
23 Feb 2017, 22:59
Shruti0805 wrote: GovindAgrawal wrote: how do we get this point of intersection? Hi, Let me try explaining. It took me a while figuring it out myself. First, we can replace the lines x=0 and y=0 by a line x=y. That leaves us with just 2 lines : 1st is x=y and 2nd is 3y= 2x + 6. To find the intersection of these 2 lines, equate the RHS variables and you'll get x=6/5. [ 2x+6 = x ]Now, substitute the value of x in either of the 2 equations and you'll get the y coordinate for the point. Does that help ? Just a little clarification. We do NOT have to replace lines x=0 and y=0 with x=y Instead we need to understand that y and x co ordinate are equL on line y=x I.e. on that line a=B But since we need b>a so we need all points above line y=x which are bounded by other three lines which are x=0 y=0 And 2x+6 = 3x I hope this helps
_________________
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



Intern
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 43
Location: Armenia
GPA: 3.4

Re: Point P(a,b) is randomly selected in the region enclosed by
[#permalink]
Show Tags
02 Aug 2018, 05:44
Bunuel , why we can not find the area of the triangle in yellow through 904545 form?
_________________
Seryozha Sargsyan 21
Contact: sargsyanseryozha@gmail.com
What you think, you become, What you feel, you attract, What you imagine, you create.




Re: Point P(a,b) is randomly selected in the region enclosed by &nbs
[#permalink]
02 Aug 2018, 05:44






