points in the plane

[success1111]

S is a set of points in the plane. How many distinct triangles can be drawn that have three
of the points in S as vertices?

(1) The number of distinct points in S is 5.
(2) No three of the points in S are collinear.

[bluementor]

You can draw a triangle if you have three distinct points that do not all lie on the same line. For example, if you have (0,0), (1,1) and (1,0), we can draw a triangle. However, if you have (0,0), (1,1) and (2,2), then you CANNOT draw a triangle since all these points lie on a single straight line.

Statement 1: 5 distinct points in set S.

We do not know if these 5 points (or at least 3 of these) lie on a single straight line. Insufficient.

Statement 2: No three of the points in S are collinear.

I believe this means no three points form a straight line. However, we don't know the number of distinct points in set S. Insufficient.

Both statements together: We know the number of distinct points, and we also know that no three points lie on the same line. Sufficient.

Choose C.

-BM-

[success1111]

You can draw a triangle if you have three distinct points that do not all lie on the same line. For example, if you have (0,0), (1,1) and (1,0), we can draw a triangle. However, if you have (0,0), (1,1) and (2,2), then you CANNOT draw a triangle since all these points lie on a single straight line.

Statement 1: 5 distinct points in set S.

We do not know if these 5 points (or at least 3 of these) lie on a single straight line. Insufficient.

Statement 2: No three of the points in S are collinear.

I believe this means no three points form a straight line. However, we don't know the number of distinct points in set S. Insufficient.

Both statements together: We know the number of distinct points, and we also know that no three points lie on the same line. Sufficient.

Choose C.

-BM-

BM,
Thanks a lot for your response.OA is C. This will definitely help.