Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Aug 2014, 21:06

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A certain computer program randomly generates equation of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 26
Schools: Babson '14
GMAT Date: 02-28-2013
Followers: 0

Kudos [?]: 6 [0], given: 56

A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 03:13
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (02:41) correct 56% (01:53) wrong based on 115 sessions
Attachment:
File comment: Given Figure
Fullscreen capture 21112012 164010.bmp.jpg
Fullscreen capture 21112012 164010.bmp.jpg [ 24.11 KiB | Viewed 2513 times ]
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.

A. 3/4
B. 3/5
C. 1/2
D. 2/5
E. 1/4
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4604
Location: Pune, India
Followers: 1043

Kudos [?]: 4572 [1] , given: 162

Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 03:43
1
This post received
KUDOS
Expert's post
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4


The thought was this:

Attachment:
Ques3.jpg
Ques3.jpg [ 9.63 KiB | Viewed 2501 times ]


Any line passing through the point P which is at 6 on the x axis will pass through one of the 4 equal dotted regions (except x axis). Out of these, lines passing through 2 of the regions are not acceptable (red lines) while those passing through other 2 are acceptable (green lines).
Hence, 1/2 of the region is fine.

Probability that the line does not pass through ABCD is 1/2.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1969
Followers: 475

Kudos [?]: 1888 [1] , given: 29

Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 12:44
1
This post received
KUDOS
Expert's post
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4

I am responding to a pm from himanshuhpr.

First of all, I am intrigued by the solution of the very intelligent VeritasPrepKarishma, for whom I have considerable respect. Nevertheless, I beg to differ.

I believe there are some significant flaws in the question. First of all, the grammar is embarrassingly atrocious, but we'll let that pass. More to the point === we are told that the program "randomly" generates lines --- how exactly is this process randomized? For example, the line goes through P --- Are all slopes equally likely? Or are all angles equally likely? If we select P and a y-intercept, are all y-intercept equally likely? Are we randomly selecting one other point in the x-y plane, and all of those points are equally likely? Those are four different ways of specifying the probabilistic process, and I believe at least some of them give different numerical answer to the question. As soon as the thing you are specifying (here, a line) can be specified in a variety of ways, its not enough to say "random" --- you have to specify exactly how the selection process proceeds.

Because the question does not specify the details of the probabilistic selection process, I believe it is a fundamentally flawed question.

Does that make sense?

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 26
Schools: Babson '14
GMAT Date: 02-28-2013
Followers: 0

Kudos [?]: 6 [0], given: 56

Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 12:59
mikemcgarry wrote:
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4

I am responding to a pm from himanshuhpr.

First of all, I am intrigued by the solution of the very intelligent VeritasPrepKarishma, for whom I have considerable respect. Nevertheless, I beg to differ.

I believe there are some significant flaws in the question. First of all, the grammar is embarrassingly atrocious, but we'll let that pass. More to the point === we are told that the program "randomly" generates lines --- how exactly is this process randomized? For example, the line goes through P --- Are all slopes equally likely? Or are all angles equally likely? If we select P and a y-intercept, are all y-intercept equally likely? Are we randomly selecting one other point in the x-y plane, and all of those points are equally likely? Those are four different ways of specifying the probabilistic process, and I believe at least some of them give different numerical answer to the question. As soon as the thing you are specifying (here, a line) can be specified in a variety of ways, its not enough to say "random" --- you have to specify exactly how the selection process proceeds.

Because the question does not specify the details of the probabilistic selection process, I believe it is a fundamentally flawed question.

Does that make sense?

Mike :-)


Mike , Thanks for replying.

I somewhat understand the flaw your are trying to point out but given the question in this ' FLAWED ' form what should be the best possible response/ method to solve the above.
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 1969
Followers: 475

Kudos [?]: 1888 [1] , given: 29

Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 15:38
1
This post received
KUDOS
Expert's post
Dear himanshuhpr,

I understand your desire to understand. As I explained in my pm response, I think this question is too flawed to admitted of an unambiguously good solution.

Instead, I created a similar question, and I believe in this question the entirely selection process of the line is very tightly defined, making the question unambiguous. Here's where it's posted ......

hard-probability-problem-lines-in-the-x-y-plane-142846.html

After some folks wrestle with it, I will post a solution.

I hope that's helpful.

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

3 KUDOS received
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 646
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 351 [3] , given: 23

GMAT ToolKit User Premium Member
Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 17:39
3
This post received
KUDOS
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4

I think the question seems to be fine and solution that Karishma provided is excellent.

If one can notice in original picture posted, cooridnates of point C ,D and P are such that angle DPC is 90. (This can be verified using coordinates or slopes)
Thus, for any line of the form y=mx+b, passing through point P. There is a 90' region from which it can not pass, else it will go inside the square ABCD. Outside of this 90 it can pass wherever it wants. it will be ok.

There is overall 180' region, starting from x-asis and going in anticlock wise, where this line can be drawn. (considering only above x-axis - as once you rotate line enough to go below x-axis, the other end of line would be above x-axis)

Thus probability = Total favourable area/Total area = 1/2

Now, coming to how it is 90' and 180'. We can consider this solution only in first quadrant or in first & fourth quadrant both. However when we consider both quadrants, since it will provide a mirror image across x-axis.
total area, which is not desired, formed by line = 90*2 and total area possible for line = 180*2 = 360

still you get same ans 1/2.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Intern
Intern
avatar
Joined: 20 Oct 2012
Posts: 5
Followers: 0

Kudos [?]: 3 [0], given: 2

Re: A certain computer program randomly generates equation of [#permalink] New post 21 Nov 2012, 18:27
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4



Interesting... while I do agree the question is poorly worded. I was able to come to (C) as the answer, but I had to recall my SIN/COS/TAN angles...which seems overkill for the GMAT. Even for a 700+ question...

Step 1:
The graph shows point P(6 units, 0 units), using either points C(4 units, 2 units) or D (8 units, 2 units) you can derive a triangle with two sides of length 2 units, and a hypotenuse we don't need to know.

Remembering SOH/CAH/TOA -> Use TOA. Tan of Angle (Degrees) = Opposite Length / Adj. Length = 2 / 2 = 1. Tan of 45 Degrees = 1.

Therefore, the sector bounded by the two linear equations is 180 - (45 x 2) = 90 degrees.

Step 2:
Realize that it will not simply be 90 / 360 (= 1 / 4) as this will include linear equations that cross ABCD.

Using the two bounded lines, visualize a North/South/East/West quadrant and realize that North/South sectors are covered by the same line equations, East/West sectors are covered by other line equations.

Probability of Lines HITTING ABCD = (Sector covered by North and South quadrant) / 360 = (90 x 2) / 360 = 1 / 2.

Probability of Lines NOT HITTING ABCD = 1 - (1 / 2) = 1 / 2.

Answer (C).
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4604
Location: Pune, India
Followers: 1043

Kudos [?]: 4572 [0], given: 162

Re: A certain computer program randomly generates equation of [#permalink] New post 23 Nov 2012, 11:21
Expert's post
I agree that the question is a little ambiguous in that it doesn't provide information on how the line is generated 'randomly' but in my opinion, the intent of the question is quite clear. The line passes through P and the angle of the line with the x axis takes a random value from 0 to 180 counterclockwise (note that it is a line so it extends indefinitely on both ends so the line making an angle of 270 degrees counterclockwise with the x axis is the same as the line making an angle of 90 degrees counterclockwise with the x axis)

Say, if the y intercept is randomly generated, the only acceptable values for the y intercept lie between 6 and -6 but y intercept can take infinite values so the options don't work in that case.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1844
Followers: 167

Kudos [?]: 33 [0], given: 0

Premium Member
Re: A certain computer program randomly generates equation of [#permalink] New post 28 Dec 2013, 09:34
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
Intern
avatar
Joined: 26 May 2013
Posts: 18
Followers: 0

Kudos [?]: 3 [0], given: 10

Re: A certain computer program randomly generates equation of [#permalink] New post 30 Dec 2013, 12:30
I took an approach similar to jcaine:

Looking at the figure, you can determine that the triangle formed by DPC has a 90 degree angle at P.

This can be assumed because triangle formed from D, (x = 4) , P is a 45-45-90 triangle. This is certain because the letters fall on distinct points within the graph. A 45-45-90 triangle is also formed by C, (x=8), P. The sides of each triangle formed here are 2-2-x SQRT 2 (45-45-90 triangle)

Using the property of a straight line = 180 degrees, you can deduct that triangle DPC has a 90 degree angle at P and any intersecting line would fall within 90 degrees out of 180.

Double that to get 180 / 360 degrees = 1/2.

Think of it as a circle and the "range" (degree) that the line can and can not pass through.

I hope this explanation helped.
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 139 [0], given: 254

GMAT ToolKit User
Re: A certain computer program randomly generates equation of [#permalink] New post 20 Feb 2014, 13:23
The extremes that cross C and D are in fact perpendicular therefore their intersection make a 90 degree angle.

Therefore 90/180 = 1/2

Answer is C

Hope it helps
Cheers
J
Senior Manager
Senior Manager
User avatar
Joined: 17 Sep 2013
Posts: 289
Location: United States
Concentration: Marketing, Strategy
GMAT Date: 04-30-2014
GPA: 3.24
WE: Analyst (Consulting)
Followers: 3

Kudos [?]: 37 [0], given: 98

GMAT ToolKit User
Re: A certain computer program randomly generates equation of [#permalink] New post 28 Apr 2014, 22:38
VeritasPrepKarishma wrote:
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4


The thought was this:

Attachment:
Ques3.jpg


Any line passing through the point P which is at 6 on the x axis will pass through one of the 4 equal dotted regions (except x axis). Out of these, lines passing through 2 of the regions are not acceptable (red lines) while those passing through other 2 are acceptable (green lines).
Hence, 1/2 of the region is fine.

Probability that the line does not pass through ABCD is 1/2.


Now I see what the Q meant to test here...Super horrible grammar..
_________________

Appreciate the efforts...KUDOS for all

Senior Manager
Senior Manager
avatar
Joined: 07 Apr 2012
Posts: 313
Followers: 0

Kudos [?]: 14 [0], given: 45

Re: A certain computer program randomly generates equation of [#permalink] New post 14 Jun 2014, 08:24
VeritasPrepKarishma wrote:
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4


The thought was this:

Attachment:
Ques3.jpg


Any line passing through the point P which is at 6 on the x axis will pass through one of the 4 equal dotted regions (except x axis). Out of these, lines passing through 2 of the regions are not acceptable (red lines) while those passing through other 2 are acceptable (green lines).
Hence, 1/2 of the region is fine.

Probability that the line does not pass through ABCD is 1/2.

Hi Karishma,

why are the four dotted areas equal probability?
How did you come about to drawing them?
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4604
Location: Pune, India
Followers: 1043

Kudos [?]: 4572 [0], given: 162

Re: A certain computer program randomly generates equation of [#permalink] New post 15 Jun 2014, 21:58
Expert's post
ronr34 wrote:
VeritasPrepKarishma wrote:
himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4


The thought was this:

Attachment:
Ques3.jpg


Any line passing through the point P which is at 6 on the x axis will pass through one of the 4 equal dotted regions (except x axis). Out of these, lines passing through 2 of the regions are not acceptable (red lines) while those passing through other 2 are acceptable (green lines).
Hence, 1/2 of the region is fine.

Probability that the line does not pass through ABCD is 1/2.

Hi Karishma,

why are the four dotted areas equal probability?
How did you come about to drawing them?


Point D coordinates (4, 2)
Point C coordinates (8, 2)
So if you extend AD and BC to touch the x axis, you get a rectangle (shown in my figure). Split it into two equal rectangles by dropping a perpendicular from P to DC. Now draw the diagonals of both rectangles as shown. Note that the diagonal of a rectangle divides the rectangle into two equal areas. Since the two rectangles were of equal areas, all four areas will be equal. Basically , you divide the entire region around point P into 4 equal areas - in 2 of them, the line will pass through the square, in 2, it will not.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: A certain computer program randomly generates equation of   [#permalink] 15 Jun 2014, 21:58
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic A certain computer program creates temporary files avohden 3 03 Dec 2013, 15:15
As part of a certain game in which a computer generated a ra manishuol 2 29 Apr 2013, 11:09
4 Experts publish their posts in the topic A certain computer program generates a sequence of numbers Nihit 13 13 Sep 2008, 06:56
A certain computer program produces anagrams by taking words amy_v 15 17 Nov 2005, 19:12
A certain computer program generates a sequence of numbers saurya_s 3 23 Sep 2004, 13:46
Display posts from previous: Sort by

A certain computer program randomly generates equation of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.