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Triangles with positive area

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by niketdoshi123 » Sat Jul 28, 2012 2:58 am
There are in total 9 integer co-ordinates satisfying 1<=x<=3 and 1<y<=3 (as shown in figure by 9 black dots)
Total # of ways of picking 3 points (vertices of the triangle) from given 9 points = 9C3 = 9!/(3!*6!) = 84

Now, we know that the three vertices of a triangle can never be co-linear.
# of such co-linear lines = 8 (As shown in figure 3 red lines, 3 blue lines and 2 yellow lines)

Hence, the # of triangles that can be drawn = 84 - 8 = 76

the correct answer is B
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by Brent@GMATPrepNow » Sat Jul 28, 2012 4:09 am
Here's a lengthy discussion on this question: https://www.beatthegmat.com/how-many-tri ... 28974.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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