Problem Solving

I like both of the above solutions, and think they are probably the most natural approaches to take here. There is at least one other way to solve the problem:

-we must choose one point from the first line (7 choices)
-we must choose one point from the second line (8 choices)
-we must choose one of the remaining points (13 choices)
-the order of the two points chosen from the same line doesn't matter (divide by 2!)

so the answer is (7*8*13)/2 = 364

You might notice that this problem is just a geometric version of this counting problem:

"A company employs 7 men and 8 women. How many different three-person committees could be formed which do not consist entirely of men or entirely of women?"

This counting problem format, where we must choose fixed numbers of things from two different groups, is very common on the GMAT.

money9111 wrote:can someone tell me the level of question this would be?

There's an identical problem (but with smaller numbers of points) in GMATFocus, and you only encounter it if you're doing quite well, so the difficulty level is certainly well above average.

Incidentally, I'm curious where the question in the post above comes from, since it is exactly the same as a real GMAT question but with slightly larger numbers.