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:

If a point P(x,y) inside the above square ABCD is chosen at [#permalink]

Show Tags

28 Aug 2006, 05:38

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

17% (05:19) correct
83% (00:53) wrong based on 11 sessions

HideShow timer Statistics

If a point P(x,y) inside the above square ABCD is chosen at random and AB is parallel to the x axis, the probability that y/x <5 is how much greater than the probability that y/x < 1/5?

(1) The midpoint of AD is (0,0).
(2) The area of ABCD is 100 square units.

I'd say (1) is sufficient and allows to say that the probability is equal, because there is abcolutely no topologic difference between x and y, so x/y < 5 is as much probable as y/x < 5. (2) is irrelevant.

Still, I'd be happy to see a 'proper' solution, mine is more of a guess.

Also, I'm not sure if we can consider AB parallel to X based on the picture; if not, (1) is insufficient.

IMO graphic approach can be used to solve the problem. Represent the inequalities as lines- y/x<5 =>y/x=5, y=5*x and y/x=1/5 => x=5y.
Now the values on the right of the first line are <5, and the values below the second line are <1/5.
Both areas are equal so A

A thing one has to realise is that everything that is < 5 of something is ALSO < 0,2 of the same thing.

Thus the probability that y/x is < 5 is only = the probability that y/x is < 0,2 if no points equal the sum of 0,2 or more.

Since the first statement is that 0,0 is in the middle and the second statement what constitutes the vertices of the box you just have to draw the box and try for yourself.

The only points that makes y/x < 0,2 are those where either x or y are negative or zero (50% of the box).

The only points that are NOT < 5 are (y=5, x= 1) and (y=-5, x=-1) since they = 5

If a point P(x,y) inside the above square ABCD is chosen at random and AB is parallel to the x axis, the probability that y/x <5 is how much greater than the probability that y/x < 1/5?

(1) The midpoint of AD is (0,0). (2) The area of ABCD is 100 square units.

Seems to be a very tough Q. Forget the probability first, to calculate Y/X we need to know the point. If we can fix the point (x,y) to a single point or to a set of points then we can calculate the probability

(1) talks about midpoint of AD. No idea bout co ordinates of any four vertices. Insuff

(2) talks about area. ie 100 SO each side = 10 and diagonal = 10 sqrt 2

Can we arrive at more than one set of vertices such that the side is 10? I think so. to arrive at 100 (square of 10) we can use (8,6) (5 sqrt 2, 5 sqrt 2)? Probably Insuff

Together we can fix the (x,y) co ordinates and can start calculating Probability, which probably is unnecessary as we will get a yes/no

From the information provided, we draw two lines: y=5x and y=1/5x

From (1) we know that square ABCD is symmetrical through point 0(0,0). So O is the centre of square ABCD. If P(x,y) is inside the square, The probability that y>5x = (the square of the the quadrilateral formed by line y=5x and the square ABCD - on the right side line y=5x) / the square of ABCD = 1/2 The probability that y>1/5x = (the square of the the quadrilateral formed by line y=1/5x and the square ABCD) / the square of ABCD = 1/2 The probability that y>5x / The probability that y>1/5x = 1

From (2) alone, we don't have enough data to answer the question.

SO THE ANSWER IS A

Please find attached the graph for your information

IMO both are needed. I used the areas method. But there is a problem it contains. We are not dealing with equalities but dealing with inequalities. Think the line y=x/5. When x and y is positive, the points between the line and the x axis gives us the (x,y) combinations in which y/x<1/5. But when we are going to the negative side. Everything changes. Think the point (-4,-1) It is under the y=x/5 line. But y/x is greater than 1/5. So the point combinations which satisfy y/x<1/5 are the points that lie between the x axis and the line. This explanation works for the line y=5x. So we can not know the exact measures of the areas that lie between the lines and the x axis only with the coordinate of midpoint. So both are needed

Let I make this right. At first, I'm sorry for making some mistakes in the figure.

Infact, the quadrilateral MBCN represents the position of P(x,y) in the square ABCD so that x>1/5y (or y/x<5)not x>5y as in the figure Similarly for the quadrilateral QCDT represents the position of P(x,y) in the square ABCD so that x>5y (or y/x<1/5)not x>1/5y as in the figure

So, the question is the probability that y/x <5 (x>1/5y) is how much greater than the probability that y/x < 1/5 (x>5y)

From (1), we have that, no matter how small or large the square ABCD, as long as it is symmetrical through center O + The probability that y/x <5 <--> (x>1/5y), given P(x,y) in square ABCD, equals (area of MBCN / area of ABCD) = 1/2 + The probability that y/x <1/5 <--> (x>5y), given P(x,y) in square ABCD, equals (area of QCDT / area of ABCD) = 1/2

Please be advised that the question does not ask us to find the point P(x,y) satisfying both inequalities y/x<5 and y/x<1/5. But it asks whether we could calculate the probability that y/x<5, given that P (x,y) is in ABCD and probability that y/x<1/5, given that P(x,y) is in ABCD.

So I think that data provided in (1) is sufficient to answer the question. And (2) alone, is not sufficient.

-points in the quadrants (x>0 and y<0) and (x<0 and y>0) are all satisfy y/x<5 and y/x < 1/5 (e.g. points (-1,3) and (2,-3) ) -points that lie over the line y=x/5 and lie under x axis are all satisfy y/x<1/5 (e.g. point (-1,-0.1) ) -points that lie over the line y=5x and lie under x axis are all satisfy y/x<5 (e.g. point (-0.1, -1) )

These do not seen in your figure anonym There is a problem in your solution.

Let I make this right. At first, I'm sorry for making some mistakes in the figure.

Infact, the quadrilateral MBCN represents the position of P(x,y) in the square ABCD so that x>1/5y (or y/x<5)not x>5y as in the figure Similarly for the quadrilateral QCDT represents the position of P(x,y) in the square ABCD so that x>5y (or y/x<1/5)not x>1/5y as in the figure

So, the question is the probability that y/x <5 (x>1/5y) is how much greater than the probability that y/x < 1/5 (x>5y)

From (1), we have that, no matter how small or large the square ABCD, as long as it is symmetrical through center O + The probability that y/x <5 <--> (x>1/5y), given P(x,y) in square ABCD, equals (area of MBCN / area of ABCD) = 1/2 + The probability that y/x <1/5 <--> (x>5y), given P(x,y) in square ABCD, equals (area of QCDT / area of ABCD) = 1/2

Please be advised that the question does not ask us to find the point P(x,y) satisfying both inequalities y/x<5 and y/x<1/5. But it asks whether we could calculate the probability that y/x<5, given that P (x,y) is in ABCD and probability that y/x<1/5, given that P(x,y) is in ABCD.

So I think that data provided in (1) is sufficient to answer the question. And (2) alone, is not sufficient.

Therefore, the answer is A.

From what you explained A makes a lot of sense.
_________________

Thank you for your kudoses Everyone!!!

"It always seems impossible until its done." -Nelson Mandela

gmatclubot

Re: DS: Probability
[#permalink]
06 Jan 2011, 07:29

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...