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Co-ordinates can be (1,1), (1,2),(1,3),(1,4) and (1,5)
similary (2,1)...(5,5)
total of 25
1. select any three from these 25
that is \(25C_3\)
but we cant select all three from (1,1), (1,2),(1,3),(1,4) and (1,5) otherwise it will be a linear line
so \(25C_3\)-5*\(5C_3\)
i am stuck after it

chetan2u can you please help what else am i missing?
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You also have to deduct the cases when 3 points lie on the diagonally straight lines. I'm getting 2160, but OA is B. :(

globaldesi
Co-ordinates can be (1,1), (1,2),(1,3),(1,4) and (1,5)
similary (2,1)...(5,5)
total of 25
1. select any three from these 25
that is \(25C_3\)
but we cant select all three from (1,1), (1,2),(1,3),(1,4) and (1,5) otherwise it will be a linear line
so \(25C_3\)-5*\(5C_3\)
i am stuck after it

chetan2u can you please help what else am i missing?
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You also have to deduct the cases when 3 points lie on the diagonally straight lines. I'm getting 2160, but OA is B. :(

globaldesi
Co-ordinates can be (1,1), (1,2),(1,3),(1,4) and (1,5)
similary (2,1)...(5,5)
total of 25
1. select any three from these 25
that is \(25C_3\)
but we cant select all three from (1,1), (1,2),(1,3),(1,4) and (1,5) otherwise it will be a linear line
so \(25C_3\)-5*\(5C_3\)
i am stuck after it

chetan2u can you please help what else am i missing?

Agree.
We are missing 12 points.

Bunuel what other points did we miss? Or is there another way to solve it

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Bunuel
How many triangles with positive area have all their vertices at points (i,j) in the coordinate plane, where i and j are integers between 1 and 5, inclusive?

(A) 2128

(B) 2148

(C) 2160

(D) 2200

(E) 2300

Official Explanation:



Attachment:
2019-05-15_0953.png
2019-05-15_0953.png [ 95.15 KiB | Viewed 3978 times ]
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Please explain the last 3 points w.r.t to slope mentioned in the solution.
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Top one is depicting lines of slope 2 and -2
Bottom one is depicting lines of slope -1/2 and 1/2

Sneha333
Please explain the last 3 points w.r.t to slope mentioned in the solution.

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IMG_20190515_144748.jpg
IMG_20190515_144748.jpg [ 3.93 MiB | Viewed 3776 times ]

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nick1816
Top one is depicting lines of slope 2 and -2
Bottom one is depicting lines of slope -1/2 and 1/2

Sneha333
Please explain the last 3 points w.r.t to slope mentioned in the solution.

Thanks Nick for the explanation.
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Bunuel
Bunuel
How many triangles with positive area have all their vertices at points (i,j) in the coordinate plane, where i and j are integers between 1 and 5, inclusive?

(A) 2128

(B) 2148

(C) 2160

(D) 2200

(E) 2300

Official Explanation:



Attachment:
2019-05-15_0953.png

i am unable to understand the point from collinear point calculation
can u elaborate pls
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Bunuel
Bunuel
How many triangles with positive area have all their vertices at points (i,j) in the coordinate plane, where i and j are integers between 1 and 5, inclusive?

(A) 2128

(B) 2148

(C) 2160

(D) 2200

(E) 2300

Official Explanation:



Attachment:
2019-05-15_0953.png

Hi the solution is spot on. I missed a few cases ie. the ones with slopes +- 1/2 and +- 2. Can we expect questions like these on the GMAT? Are they not tad bit more time consuming and calculation intensive?
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