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Let S be the set of points (a, b) in the coordinate plane, where each

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Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 21 Mar 2019, 04:52
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  95% (hard)

Question Stats:

26% (02:18) correct 74% (01:59) wrong based on 42 sessions

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Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 21 Mar 2019, 09:33
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Bunuel wrote:
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


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
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Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 24 Mar 2019, 13:49
Archit3110 wrote:
Bunuel wrote:
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


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


Can you please elaborate the process for counting lines passing through 3 points?

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Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 25 Mar 2019, 02:56
Archit3110 wrote:
Bunuel wrote:
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


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



Could you please elaborate 2nd part of the explanation.. It's a bouncer for me.
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Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 25 Mar 2019, 10:21
chetan2u please can you explain how to crack this one ?
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Re: Let S be the set of points (a, b) in the coordinate plane, where each  [#permalink]

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New post 25 Mar 2019, 21:07
Bunuel wrote:
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



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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Re: Let S be the set of points (a, b) in the coordinate plane, where each   [#permalink] 25 Mar 2019, 21:07
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