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 500,000 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:

50% (02:13) correct
50% (02:21) wrong based on 109 sessions

HideShow timer Statistics

In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?

The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B.
_________________

Re: In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

20 Jul 2016, 02:22

MathRevolution wrote:

In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?

A. 1/2 B. 1/3 C. 1/4 D. 2/3 E. 3/4

* A solution will be posted in two days.

Quote:

Sir, This attachment that you have in the problem. Is that information GIVEN or you have derived that drawing based on the information provided in the following question: In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), and C(0,12). If a point (x,y) is in the triangle ABC, what is the probability that y is smaller than x?

Re: In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

13 Jan 2017, 06:19

Y would be smaller than x, if the point lies within triangle OBC, i.e., between the lines OB and OC of the given diagram. C is the intersection AB and OC. To find the coordinates of C we need to solve the equation of AB and OC.

The equation for AB: \(y=ax+b\). Slope of AB is -2, y intersection is 6.

\(∴y=-2x+6=>y+2x=6-------(i)\)

The equation for OC: \(y=x-----(ii)\)

Solving equations (i) and (ii) we get x and y coordinates of point C, x = 4 and y = 4

So, the area of triangle OCB is 4 = 12 and the Area of triangle OAB is 36.

∴ The probability is \(\frac{12}{36}=\frac{1}{3}\)
_________________

In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

26 Aug 2017, 20:57

MathRevolution wrote:

The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B.

It is given y should be less than x , Would this solution account for the integer values where y=x ??

Re: In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

26 Aug 2017, 23:23

1

This post received KUDOS

Siddhuftr wrote:

MathRevolution wrote:

The probability of y<x is same as the area of △OBC/the area of △OBA. Since the lower base=OB=6, we get a/12. Also, if we substitute this into 2x+y=12, we get 2a+12. From this we get a=4. Then, we obtain a/12=4/12=1/3. Hence, the correct answer is B.

It is given y should be less than x , Would this solution account for the integer values where y=x ??

Hello siddhuftr

From the triangle x and y can take non integer values as well , no where it is mentioned about integer values. You have to consider all points in that area. Hope its clear.

Re: In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

21 Sep 2017, 01:43

Hi,

attached is how I approached it, and got 1/2 instead of 1/3. General approach seems to be correct, but I am thinking that the area of smaller triangle shoul be 18, not 12, because the question asks for situation where Y (= height) is less than X (=base), so I drew a triangle (shaded area), where base = 6, height =6.

Where am I wrong with this?? Please enlighten me!! Bunuel

In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0), [#permalink]

Show Tags

21 Sep 2017, 02:38

HappyQuakka wrote:

Hi,

attached is how I approached it, and got 1/2 instead of 1/3. General approach seems to be correct, but I am thinking that the area of smaller triangle shoul be 18, not 12, because the question asks for situation where Y (= height) is less than X (=base), so I drew a triangle (shaded area), where base = 6, height =6.

Where am I wrong with this?? Please enlighten me!! Bunuel

Thank you so much in advance!

Your x,y coordinate of point F are wrong. I dont know how you got 6,6 => can you explain how you got 6,6?? and the correct coordinate will be 4,4
_________________

Give Kudos for correct answer and/or if you like the solution.

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...