There are three parallel straight lines

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 31
Joined: 23 Oct 2013
Thanked: 2 times
Followed by:1 members
GMAT Score:750

There are three parallel straight lines

by mensanumber » Tue Mar 06, 2018 11:55 pm
There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. What is the maximum number of triangles that can be drawn from these points?

1) 41
2) 40
3) 18
4) 44

User avatar
GMAT Instructor
Posts: 15533
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1901 members
GMAT Score:790

by GMATGuruNY » Wed Mar 07, 2018 11:21 am
mensanumber wrote:There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. What is the maximum number of triangles that can be drawn from these points?

1) 41
2) 40
3) 18
4) 44
From the 6 points, ANY COMBINATION OF 3 can serve to form a triangle.
Thus:
Maximum number of triangles that can be formed from the 6 points = number of ways to choose 3 points from 6 options = 6C3 = (6*5*4)/(3*2*1) = 20.

The correct answer does not seem to be among the answer choices.
What is the source?
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3