Register    Login    Search    Rss Feeds

 Page 1 of 1 [ 2 posts ] 



 
Author Message
 Post subject: A certain square is to be drawn on
 Post Posted: Wed Jun 06, 2012 5:18 pm 
Offline
Course Students


Posts: 2
Cat Exam #4 Question 12:
"A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?"

Answer is 12. Explanation discusses pythagorean triple and why a line with a vertice at the origin could have it's other vertice at (0,10), (6,8), (8,6),... I understand that part, and why there would then be 12 options. What I don't understand is how you can assume from that explanation that the other vertices of the square will also be integers. The explanation only says that "It is tedious and unnecessary to figure out all four coordinates for each square" but I don't see how it necessarily follows that the other vertices will also be integers just because one is. Please explain.


Top 
 Post subject: Re: A certain square is to be drawn on
 Post Posted: Fri Jun 08, 2012 3:40 am 
Offline
ManhattanGMAT Staff


Posts: 5074
Location: Southwest Airlines, seat 21C
draw them out for yourself if you're skeptical. you'll probably see after the first square or two that it becomes obvious to you that all the other vertices will be integers..

_________________
Tim Sanders
Manhattan GMAT Instructor


Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 2 posts ] 





Who is online

Users browsing this forum: No registered users and 0 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: