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21 Mar 2019, 04:52
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:25) correct
67%
(02:12)
wrong
based on 101
sessions
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Not Attempted Yet
Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many distinct lines pass through at least two members of S?
(A) 8
(B) 20
(C) 24
(D) 27
(E) 36
(A) 8
(B) 20
(C) 24
(D) 27
(E) 36
Archit3110
21 Mar 2019, 09:33
Kudos
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Bunuel
total pairs of points which can be formed is 9
and line passing through 2 such points 9c2 = 36
we have overcounted all of the lines which pass through three points. In fact, each line which passes through three points will have been counted 3c2 = 3 times
3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20
IMO B
25 Mar 2019, 21:07
Kudos
Bookmarks
Bunuel
The points should tell you that you are looking at a square with coordinates (-1,-1), (-1,1), (1,1) and (1,-1). The centre of the square and midpoint of each side are other points..
So, in total we have 9 points. But, the centre will always be part of 3 points.
So we are left with 8 points, and we have to choose 2 out of it, so 8C2=8*7/2=28.
Now, the sides of the square consists of 3 points. We have counted each side thrice, so 4*2 are repeated. Thus, 28-8=20.
For example.. side containing points A(-1,-1), B(-1,0) and C(-1,1).. The line is only one but we have calculated it thrice in our calculations. AB, BC and AC, whereas it is just on eline AC.
B
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