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Right triangle PQR is to be constructed in the xy-plane so

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Re: Right triangle PQR is to be constructed in the xy-plane so  [#permalink]

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New post 09 Jun 2018, 04:54
teaserbae wrote:
Any 3 points on a plane can't form a triangle.
But in this question, any 3 points seem to make a triangle, I just wanted to know the proof behind that


Hey teaserbae

You seemed to have misunderstood a plane for a line. Any 3 points on a line cannot
form a triangle. On the contrary, any 3 points on a plane can form a triangle.

Definition of a plane:
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is
the two-dimensional analogue of a point(zero dimensions), a line (one dimension) and three-dimensional space.


Hope this helps you!
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Re: Right triangle PQR is to be constructed in the xy-plane so  [#permalink]

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New post 04 Sep 2018, 07:33
Could we not just see that we have 9 possibilities for R when we constrain P and Q, and since this is a combinatorics problem, understand that the answer will be derived from a multiplicative relationship? Therefore, the answer must be a multiple of 9 - hence, C.
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Right triangle PQR is to be constructed in the xy-plane so  [#permalink]

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New post 06 Sep 2018, 03:54
Bunuel wrote:
abdullaiq wrote:
Could someone please explain how those numbers came out? Where did the 11, 10, and 9 came from? There is no specific point for them.

gettinit wrote:
yes can someone please explain in detail please? Thanks


Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed?
A. 110
B. 1100
C. 9900
D. 10000
E. 12100

We have the rectangle with dimensions 10*11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.

Choose the (x,y) coordinates for vertex P (right angle): 10C1*11C1;
Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10-1=9 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11-1=10 as 1 vertical dot is already occupied by A).

10C1*11C1*9C1*10C1=9900.

Answer: C.

Other discussion with alternate solutions:
http://gmatclub.com/forum/arithmetic-og ... ed#p790651
http://gmatclub.com/forum/geometry-and- ... ed#p777591
http://gmatclub.com/forum/700-question- ... ed#p818546

Hope it helps.

Hi Bunuel i would to take this question as an opportunity to ask you few questions. Today i have formally started my preparation for quant i have read all MGMT maths books and Gmat club math book my concepts are fine and this is my first 700+ and oG tag question but the real problem i am facing is the time management such as in this question i was unable to find a concrete procedure and it took me 5 min to sort the matter out and find discreetly what the question was asking. i would like to know that is there any specific pattern in quants that keep on repeating in a different creative way so that one dont waste time sorting out the method but rather recognize the pattern and slove it. just like the chess puzzle or i would put it in another way, how solving this question is helping me in quant practice. Furthermore should i practice 700+ questions only or should i go for 600-700 range as well.
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Right triangle PQR is to be constructed in the xy-plane so &nbs [#permalink] 06 Sep 2018, 03:54

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Right triangle PQR is to be constructed in the xy-plane so

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