well done. i have only two things to add, and both of them are somewhat nitpicky.
one (emphasis mine):
parallel_chase wrote:Statement I
5 distinct points, triangles formed = 5c3 = 10, but we dont know how many points are collinear. Therefore Insufficient.
actually, that's not the number of triangles formed. that's the
number of distinct sets of three points.
ironically in this case, the whole crux of this statement's being insufficient is that you don't know whether all of these sets of points actually represent triangles. in particular, if you get 3 points that are lined up, then you'll get a straight line instead of a triangle.
also, you don't actually have to compute the combinatorial formula (and indeed you shouldn't, unless such computations are straightforward and easy for you). instead, you can just consider the following 2 extreme cases:
(a) all 5 points are in a straight line**. total = 0 triangles.
(b) none of the points are lined up. total = definitely more than 0 triangles.
therefore, insufficient.
**notice that it should be easier to realize that this particular issue matters, because the other statement alludes to it.
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two:
No 3 points collinear, 5 distinct points, distinct triangles = 5C3 = 10.
again, note that there's no need to perform the actual combinatorial computation here; indeed, it's a waste of time, unless you find such computations straightforward and easy.
you can just realize that there are 5 points, none of which are lined up, and so there must be some fixed # of combinations of those points. it's the same as picking 3 books from a set of five: even if you don't know how to compute the number right away, it's good enough just to figure out that the number exists in the first place.
Ron has been teaching various standardized tests for 20 years.
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