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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Line L passes through (5,0) and (0,10).If a point is [#permalink]
10 Mar 2008, 08:45

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Line L passes through (5,0) and (0,10).If a point is selelcted at random from the triangular region encircled by axis-x, axis-y, and line L, what is the probability that y<x?

Re: PS (probability) [#permalink]
10 Mar 2008, 09:01

I am not sure about exact answer.

Area of Whole traingle = 1/2*5*10 = 25 Area of triangle Between Y > 5 and Y <= 10 = 1/2*5*5 = 12.5 In second traingle all the values of Y will be greater than X so Prob. for Y > X = 12.5/25 = 1/2

However there will be case in which Y>X even within the lower triangle so I am not sure how to handle them. E.g. (1,4) is valid point in lower triangle here Y>X so such probability also needs to be accounted for.

I can say that probability of X>Y will be around 1/4. So I will go by the answers rather than doing the whole calculations.

Re: PS (probability) [#permalink]
10 Mar 2008, 15:58

2

This post received KUDOS

As Abhijit said, the whole triangle is 25. The fraction of this larger triangle having points where y<x are contained in the smaller triangle whose sides are the x axis, the line having points (0,10) and (5,0), and the line y=x. The line y=x intersects the line with points (0,10)(5,0) at (10/3, 10/3):

y-10=(-10/5)(x-0) (Point slope form of line between 0,10 and 5,0) y-10=(-2)(y) (sub y=x) 3y=10

The area of the smaller triangle is 1/2 * 5 * 10/3 = 25/3 The ratio of the smaller triangle to the larger is (25/3)/25 = 1/3 The probability is 1/3 that y<x

Re: PS (probability) [#permalink]
10 Mar 2008, 19:24

tritium6 wrote:

The fraction of this larger triangle having points where y<x are contained in the smaller triangle whose sides are the x axis, the line having points (0,10) and (5,0), and the line y=x. The line y=x intersects the line with points (0,10)(5,0) at (10/3, 10/3):

Awesome.... +1.

Like an idiot I drew a straight line parallel to x axis intersecting at 5 on the y-axis as the splitting point.... _________________

Re: PS (probability) [#permalink]
10 Mar 2008, 20:06

az780 wrote:

Line L passes through (5,0) and (0,10).If a point is selelcted at random from the triangular region encircled by axis-x, axis-y, and line L, what is the probability that y<x?

Please kindly provide explanation.

Imagine you create a full square here. We have 5*10=50 possible points. Now the ways we can have y<x are (assuming integer values)

1,0 2,0 3,0 4,0 5,0

2,1 3,1 4,1 5,1

3,2 4,2 5,2

4,3 5,3

5,4

15 ways

15/50 = 3/10 aprox???

gmatclubot

Re: PS (probability)
[#permalink]
10 Mar 2008, 20:06