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# How many triangles possible?

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Intern
Joined: 05 Feb 2009
Posts: 7

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27 Feb 2009, 05:15
Right triange PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed??

A 110
B 1100
C 9900
D 10000
E 12100

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Intern
Joined: 23 Feb 2009
Posts: 6
Re: How many triangles possible?  [#permalink]

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27 Feb 2009, 08:14
E
different variants for x: 4+5+1=10 (4 negative points, 5 positive and zero)
different variants for y: 16-6+1=11 (top coordinate - bottom coor. + 1..can't explain, count with fingers )
PR parallel to ox, so we need different variants for x: for 2 points P and Q
PQ parallel to oy, ... P and R
so all possible triagles ... 10*10*11*11 = 12100
Director
Joined: 04 Jan 2008
Posts: 818
Re: How many triangles possible?  [#permalink]

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27 Feb 2009, 08:23
awesome Q
post505777.html
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http://gmatclub.com/forum/math-polygons-87336.html
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Intern
Joined: 23 Feb 2009
Posts: 6
Re: How many triangles possible?  [#permalink]

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27 Feb 2009, 08:28
oops! i was wrong
C) 9900

10*9*11*10=9900 (for P and R points - same x-coordinate...but for third point 9..if 10 it will be line, not triangle... and the same for y-coord!)
Manager
Joined: 27 Feb 2009
Posts: 57
Re: How many triangles possible?  [#permalink]

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27 Feb 2009, 12:20
Hey can you please explain it clearly. I totally got lost, when you are finding the next 10 and 11. Sorry for the trouble.
Intern
Joined: 07 Oct 2008
Posts: 12
Re: How many triangles possible?  [#permalink]

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28 Feb 2009, 03:33
Even I am missing some combinations not sure where
I am getting only 990...
SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York
Re: How many triangles possible?  [#permalink]

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28 Feb 2009, 13:07
1
think this way.

assume x values are
(x1,.... x10)
Y values are
(y1,.... y11)

you need three points to form a triangle.

(x1,y1) , (x1,y2) (x2 y1) form a triangle.

--> that means you need to select two points (x1,x2) from x series and two points (y1,y2) from y series.

Select two points from x series = 10P2 (since order does matter.. it should be permuation)
Select two points from y series = 11P2
Answer = 11P2 *10P2 = 11*10 * 10*9 = 9900

I hope you got it.
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Manager
Joined: 27 Feb 2009
Posts: 57
Re: How many triangles possible?  [#permalink]

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28 Feb 2009, 17:02
Thanks x2suresh...got it
Intern
Joined: 07 Feb 2009
Posts: 46
Re: How many triangles possible?  [#permalink]

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02 Mar 2009, 04:22
Nice explanation x2suresh, it is now clear to me.
+1 from me.

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This is not a quality discussion. It has been retired.

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Re: How many triangles possible? &nbs [#permalink] 02 Mar 2009, 04:22
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# How many triangles possible?

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