Triangles with positive area

Expert replies

Phoenixvikas: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Jun 29, 2012 9:41 pm; Thanked: 2 times

by Phoenixvikas » Sat Jul 28, 2012 1:49 am

How many triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x, y) satisfying 1<=x<=3 and 1<=y<=3?

(A) 72
(B) 76
(C) 78
(D) 80
(E) 84

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jul 28, 2012 1:49 am

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

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

Attachments

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review