but what abt the combination (1,1)(2,2)& (3,3). they alo create the a straight line combination.
?
why cant answer be - 76 ?
pls clarify
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How many triangles on the coordinate plane
but what abt the combination (1,1)(2,2)& (3,3). they alo create the a straight line combination.
?
why cant answer be - 76 ?
pls clarify
?
why cant answer be - 76 ?
pls clarify
but what abt the combination (1,1)(2,2)& (3,3). they alo create the a straight line combination.
?
why cant answer be 76 ?
as there are 8 points that make straight lines.
pls clarify
?
why cant answer be 76 ?
as there are 8 points that make straight lines.
pls clarify
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Brent@GMATPrepNow
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The answer is 76.commonashish wrote:but what abt the combination (1,1)(2,2)& (3,3). they alo create the a straight line combination.
?
why cant answer be 76 ?
as there are 8 points that make straight lines.
pls clarify
Here's my full solution:
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
There are 9 dots , (x,y) values from which we need to choose 3 to form a triangle. 3C9=84 we have to reduce the dots that are on the same line 3 on y axis, 3 on x axis, 2 diagonals.
Answer = 84-8=76
Answer = 84-8=76
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Brent@GMATPrepNow
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Because we are limiting the vertices to integer coordinates only.Imsukhi wrote:Hey! Can come one explain how come there are 9 points in the plane ?
These coordinates, (x,y), must satisfy 1 ≤ x ≤ 3 and 1 ≤ y ≤ 3
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
76 is the correct answer.
9 possible points, we need to choose 3 out of 9 where order is not important so: 9!/(6!*3!)=84
now we need to omit those 3 points which can't make a triangle, i.e. 8 of the 84 possible selections, Therefore the right answer is 84-8=76
9 possible points, we need to choose 3 out of 9 where order is not important so: 9!/(6!*3!)=84
now we need to omit those 3 points which can't make a triangle, i.e. 8 of the 84 possible selections, Therefore the right answer is 84-8=76
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ganeshrkamath
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The coordinate range gives a total of 9 points.Brent@GMATPrepNow wrote:How many triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3?
(A) 72
(B) 76
(C) 78
(D) 80
(E) 84
So any three points which are not collinear form a triangle.
So the required number = 9C3 - 8 = 9*8*7/6 - 8 = 76
Choose B
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GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
GMAT/MBA Expert
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Brent@GMATPrepNow
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- Posts: 16207
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The slot method (aka applying the Fundamental Counting Principle) doesn't really work here because the outcomes of each stage/slot do not differ. For example, selecting (1,2) for the first vertex, is the same as selecting (1,2) for the second vertex.stevennu wrote:How would the slot method look in solving this type of question?
For more about this, please see https://www.beatthegmat.com/mba/2013/09/ ... s-part-iii
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
There are 9 points in the 1st quadrant. Hence 9C3 combinations are possible with these points.
9C3=84.
But as lines which come on a straight line cannot from a triangle and there are 8 such lines, these must be subtracted from the total.
a b c
d e f
g h i
where (a,b,c), (a, d,g), (g,h,i), (c,f,i), (a,e,i), (c,e,g), (d,e,f) and (b,e,h) are the 8 combinations where a triangle cannot be formed
Hence the answer must be 84-8 = 76
9C3=84.
But as lines which come on a straight line cannot from a triangle and there are 8 such lines, these must be subtracted from the total.
a b c
d e f
g h i
where (a,b,c), (a, d,g), (g,h,i), (c,f,i), (a,e,i), (c,e,g), (d,e,f) and (b,e,h) are the 8 combinations where a triangle cannot be formed
Hence the answer must be 84-8 = 76
Hi there,
So I realize this post is super old, but I've just began preparing myself for to take the GMAT in 2014 and Quant is what I most need to focus on. Is there anyone who might be able to explain the rationale behind these calculations to me in a way that a person without extensive Quant background could understand?
Thanks a million in advance!
So I realize this post is super old, but I've just began preparing myself for to take the GMAT in 2014 and Quant is what I most need to focus on. Is there anyone who might be able to explain the rationale behind these calculations to me in a way that a person without extensive Quant background could understand?
Thanks a million in advance!
