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CO ordiates !

This topic has 1 expert reply and 3 member replies
vishubn Legendary Member Default Avatar
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CO ordiates !

Post Fri Oct 24, 2008 8:33 pm
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA C
I think DS is wat i screw up Sad

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reacher Newbie | Next Rank: 10 Posts Default Avatar
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Post Sun Oct 26, 2008 6:28 am
[quote="vishubn"]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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

This question is asking you to recollect the fundamental ideas in geometry, especially the postulates. Earlier quotes have caught the fish for you but it will be better if you learn how to catch it yourself. You know that there are "postulates: a postulate is a statement that is assumed true without proof" and "theorems: a true statement that can be proven" in geometry.

There are six postulates:
1. A line contains at least two points.
2. A plane contains at least three noncollinear points.
3. Through any two points, there is exactly one line.
4. Through any three noncollinear points, there is exactly one plane.
5. If two points lie in a plane, then the line joining them lies in that plane.
6. If two planes intersect, then their intersection is a line.

The question above is giving you the hints of the postulates in disguised form. Read these postulates with the explanation given by earlier quotes and I am sure you will see the fish biting your bait.

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Post Sat Oct 25, 2008 8:46 pm
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.

--

two:
Quote:
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.

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logitech Legendary Member
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Post Sat Oct 25, 2008 12:40 am
vishubn wrote:
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.

OA C
I think DS is wat i screw up Sad
Vishbun:

(2) is insuf because it has no numbers in it! SO you can eliminate B and D

now you have check whether (1) is sufficient and remember even you have to guess, you increased your chances from 20 % to 33 % just by eliminating the easy statement.


(1) gives you some numbers but you don't know how those points are distributed in XY plane ? what if there are all in same line


. . . . .

So you still can't decide. You can eliminate A too.

Now your chances are 50 % - 50 %

Is it C or is it E ?

Well if you combines both statements, you have the number information and you know how they are respect to eacther

Go with the C!

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parallel_chase Legendary Member Default Avatar
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Post Sat Oct 25, 2008 12:46 am
vishubn wrote:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA C
I think DS is wat i screw up Sad
The answer is Indeed C.

I guess you got confused by the word "collinear"
Collinear mean when two or more points lie on the same line


Statement I
5 distinct points, triangles formed = 5c3 = 10, but we dont know how many points are collinear. Therefore Insufficient.

Statement II
no 3 points are collinear, but we dont know how many points does set S have. Insufficient.

Combining I & II

No 3 points collinear, 5 distinct points, distinct triangles = 5C3 = 10.

Hope this helps.

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