Problem Solving

but what abt the combination (1,1)(2,2)& (3,3).

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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.

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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 ?

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

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

Hey! Can come one explain how come there are 9 points in the plane ?

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

9C3-3*2-2*1=76

3*2 for 2 sets of 3 parallel lines.

2*1 for the 2 diagonals.

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

The coordinate range gives a total of 9 points.
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

Cheers

How would the slot method look in solving this type of question?

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

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!