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

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

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16 Jul 2015, 09:33
there are 10 points on the x axis from which we can choose any twos and then form the desired PR base.

By the same way ,there are 11 points on the y-axis from which we can choose any twos and then form the desired PQ perpendicular.

We can form 10P2 * 11P2=9900
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Re: Right triangle PQR is to be constructed in the xy-plane so  [#permalink]

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07 Jan 2017, 14:19
This was a very hard question for me.

I know that the set of vertices that should satisfy the inequalities apply to all P,Q and R. I took a look at the options and noticed only C that could be divisible by 3.. since set of all the vertices/3. Hence picked C.
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Right triangle PQR is to be constructed in the xy-plane so  [#permalink]

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29 Apr 2018, 08:14
Bunuel wrote:
gmatJP wrote:
Can anyone please tell me how to figure this out...

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

thanks..

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.

Bunuel two questions

why do you mention rectangle, wheras the question is about right triangle

and another question why here do you mupliply x by y Choose the (x,y) coordinates for vertex P (right angle): 10C1*11C1;

whereas in the below two steps you dont multiply what is the logic ?

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).

thank you
Right triangle PQR is to be constructed in the xy-plane so &nbs [#permalink] 29 Apr 2018, 08:14

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