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:

Re: need help counting prob with geometry [#permalink]

Show Tags

21 Aug 2010, 12:30

Answer is 4 If area is 100 than to calculate length of the side of area:10 Co-ordinates Square1 (0,0),(10,0)(10,10)(0,10) Co-ordinates Square2 (0,0),(-10,0)(-10,-10)(0,-10) Co-ordinates Square3 (0,0),(-10,0)(-10,10)(0,10) Co-ordinates Square4 (0,0),(10,0)(10,-10)(0,-10)

Let me know If you didn't get it
_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed." - Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

4 apparent squares; with one of the vertices as: (0,10),(10,0),(-10,0)(0,-10).

Then, I took the square in the first quadrant and slowly moved anticlockwise.

I could guess that finding integral co-ordinates for just one of the other vertices in the square( other than 0,0) would suffice and I did find all the required points, {(8,6),(6,8)(-6,8)(-8,6)(-8,-6)(-6,-8)(6,-8)(8,-6)} using pythagoras theorem.

However, I still couldn't formulate how the remaining two points will be integers as well.

By what principle of Geometry can we conclude that, in an xy plane; if two points of a square are integers, such as (0,0) and (8,6); the other two vertices will be all integers as well without explicitly solving for specific values of those vertices.
_________________

fluke Principle of the triplets. 3:4:5 or 6:8:10. Karishma's assumptions are correct. She is the best.

8 squares are obvious and NOT tilted. With one vertex on the origin. 4 are tilted with diagonals on the x and y axis. With one vertex on the origin.

Hope that helps ! Btw if this question comes in real exam, I will recall that answer is 12.

fluke wrote:

By what principle of Geometry can we conclude that, in an xy plane; if two points of a square are integers, such as (0,0) and (8,6); the other two vertices will be all integers as well without explicitly solving for specific values of those vertices.

This is doable in a minute or so. 4 on the vertices should come fairly quickly. Then, once you realize that 10 is a multiple of a 3-4-5 triagle, you should recognize more are possible. I drew just one, by arbitrarily picking one to draw. My choice was (-6, -8) from the origin. Recognize that You can do the same shape in the other four quadrants, and can flip to (-8, -6). 12 total.

We can draw 12 squares with one vertix at the origin. The regular 4 squares with all vertices on the x and y coordinates - 4 squares Tilt the side of a square to 45 degrees - 4 squares Tilt the side of the square to 60 degrees - 4 squares

Can you post a diagram and explain. I dont think your answer is right.

With 45 degree the diagonal will lie ong the X aix.

The co-ordinates of diagonal on X aixs will be (0,0) and (10\sqrt{2} , 0)
_________________

If you liked my post, please consider a Kudos for me. Thanks!

I am totally confused, shouldn't x and y be the same as it is a square and there are only 4 possibilities. Isn't it (+/- 10, 10) and (10, +/- 10)? Help Please!
_________________

For the square to have an area of 100, the length of any one side of the square must be 10.

For this to be true, if one vertex of the square is given to be the origin (0,0) then we can take one vertex adjacent to this vertex as (x,y)

For the length of this vertex to be 10, using the distance formula, sqrt [(x-0)^2 + (y-0)^2] = 10 => x^2 + y^2 = 100

Therefore the possible coordinates of the adjacent vertex are the values of x and y which satisfy this equation. There are 12 such values (as detailed above), so there are 12 possible squares.

Note that (10,10) is not a solution for a vertex adjacent to (0,0) as its distance from (0,0) is not 10.
_________________

Thank you very much Gyanone. Yes, (6,8) and (0,0) don't make the diagonal but one of the sides of the square. I got it now. Thank you again for the explanation.
_________________

Hey dude I am not getting how you come with (6,8) and (8,6) as valid vertices point.

As per my knowledge... if we have one vertices to be (0,0) then one of vertices will lie on X axis (10,0) and other one must lie on Y axis (0,10) ..

So we are left with only one choice for fourth vertices... (10,10)

This is for 1 quadrants , as we have total 4 quadrants answer should be 4 .

Hope i have not done anything wrong here and i had understand question.

Please correct me if i am wrong

Thanks Vishal Shah

Distance between (0,0) and (6,8) or (8,6) will be 10.

And this distance will make the side of square. So do I think that the answer is 12 (3 square in 4 areas)

I still don't understand. The distance between (0,0) and (6,8) equals to 10 - you're right, but area of the square is not 100, but 48. Or where am I mistaken? 4 is correct IMO.

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

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...