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by GHong14 » Fri Jun 03, 2011 12:58 pm
Right Triangle 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 integers that satisfy the inequalities -4 <= x <= 5 and 6<=y<=16. How many different triangles with these properties could be constructed?

110
1100
9900
10000
12100
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by cans » Fri Jun 03, 2011 4:51 pm
https://www.beatthegmat.com/right-triangle-t84347.html
This is the same question discusssed
IMO C
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by galaxian » Fri Jun 03, 2011 5:09 pm
X coordinate can have a total of : 5 - (-4) + 1 = 10 coordinates [+1 coz both inclusive]
Y ...................................: 16 - 6 + 1 = 11 Coordinates

So for any X & Y coordinate to lie in this range, we have this possibility :

10C2 * 11C2


Since, X coordinate of P = X coordinate of R.
Similarly, Y coordinate of P = Y coordinate of Q. [As PR is parallel to X Axis & PQ parallel to Y Axis]

We have a total of 4 x & y coordinates with us to be placed.

Hence, 10C2 * 11C2 * 4 = 9900

So OA should be C
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by galaxian » Fri Jun 03, 2011 5:11 pm
@cans Ah Great I didn't notice that !
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by GHong14 » Fri Jun 03, 2011 6:33 pm
Very elegant
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