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divyamurali
Joined: 07 Nov 2016
Last visit: 06 Sep 2022
Posts: 6
Given Kudos: 33
Location: India
Schools: Great Lakes '19 (A)
GMAT 1: 620 Q47 V29
GPA: 3.9
26 Aug 2017, 00:07
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I think the answer is B and the exact answer for this will have 3 conditions.
Total no of points= 8 points
but 3 collinear points
1. 3 points to make the triangle is from the 5 points which are not collinear
5C3
2. 3 points to make the triangle is from 1 vertex from 3 collinear set and 2 vertex from 5 points set
3C1 * 5C2
3. 2 vertex of the triangle can be from the same collinear line as they can act as base and the 3rd vertex from the other 5 points
3C2 * 5C1
1+2+3= 5C3+3C1*5C2+3C2*5C1
Total no of points= 8 points
but 3 collinear points
1. 3 points to make the triangle is from the 5 points which are not collinear
5C3
2. 3 points to make the triangle is from 1 vertex from 3 collinear set and 2 vertex from 5 points set
3C1 * 5C2
3. 2 vertex of the triangle can be from the same collinear line as they can act as base and the 3rd vertex from the other 5 points
3C2 * 5C1
1+2+3= 5C3+3C1*5C2+3C2*5C1
01 Nov 2017, 02:11
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Let's name each of 8 points as a,b,c,d,e,f,g,h
Let's assume that a,b&c are in one straight line, so cannot form a triangle with each other.
Now, total possible Triangle that can be formed choosing any 3 points without any colinear constraint is 8C3 = 56.
Now, out of 56 possible sets of 3 points each, there is one set a-b-c that is incapable of forming a triangle. But, remaining 55 triangle are possible.
Hence, Statement 2 is sufficient and Ans is B.
Posted from my mobile device
Let's assume that a,b&c are in one straight line, so cannot form a triangle with each other.
Now, total possible Triangle that can be formed choosing any 3 points without any colinear constraint is 8C3 = 56.
Now, out of 56 possible sets of 3 points each, there is one set a-b-c that is incapable of forming a triangle. But, remaining 55 triangle are possible.
Hence, Statement 2 is sufficient and Ans is B.
Posted from my mobile device
27 Feb 2019, 02:45
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flyingbunny
Thanks for the concise answer!
I have one question, tho.
Isn't there a condition in making a triangle?
Such as "The added length of 2 sides of a triangle has to be longer than the last side."
How can we rule out this condition?
