Consider the five points comprising of the vertices of a square and th

Question

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

(A) 4 
(B) 6
(C) 8 
(D) 10
(E) 12

Vivor · Answer

Out of the 5 points, any 3 could be chosen to form a triangle.

Hence, Ans = 5C3 = \frac{5!}{(5-3)!*3!} = 10

Ans is D IMO

Kanwarinder · Answer

You are assuming all points lie on different plane. there are 2 combinations that form a straight line so correct answer should be 10-2 = 8

gmatuser523 · Answer

If you draw a square with diagonal lines in the middle, you will see 4 triangles can be created by default, with one vertex being the center. Label the points, 1, 2, 3, 4 and 5 (diagonal intersection). You can form 4 from point 5 and 2 other points. You can form another 4 visually by counting the 4 right angle triangles. That adds to 8.

If you go the combinatorics route and got 10, you have to subtract 2 because 2 of the options are straight lines with 3 points, and those are not triangles which gives you 8

If you go the combinatorics route and got 10, you have to subtract 2 because 2 of the options are straight lines with 3 points, and those are not triangles which gives you 8

Consider the five points comprising of the vertices of a square and th

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Consider the five points comprising of the vertices of a square and th

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