Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Right triangle PQR is to be constructed in the xy-plane so [#permalink]
13 Oct 2008, 02:13

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

65% (02:21) correct
34% (02:00) wrong based on 185 sessions

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 inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?

Re: PS : RIGHT TRIANGLE PQR [#permalink]
10 Dec 2010, 00:01

7

This post received KUDOS

Expert's post

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).

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 inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?

(A) 110 (B) 1,100 (C) 9,900 (D) 10,000 (E) 12,100

I just plotted 10 horizontal points and 11 vertical points and solved it using the following formula:

(11-1)*(10-1)*11*10 = 10*9*11*10=9900 Matched with Bunuel's approach and found the logic was pretty similar.

If you plot the points; you would see that you can make 90 right triangles at every point. Then, just multiply this figure with the total number of points.

Right triangle PQR is to be constructed in the xy-plane [#permalink]
03 Jul 2013, 10:21

1

This post received KUDOS

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at Pand PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and Rare to be integers that satisfy the inequalities -4 <= x =<5 and 6=<y =<16. How many different triangles with these properties could be constructed? (A) 110 (B) 1,100 (0 9,900 (D) 10,000 (E) 12,100

Re: Right triangle PQR is to be constructed in the xy-plane [#permalink]
03 Jul 2013, 11:44

Expert's post

akijuneja wrote:

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at Pand PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and Rare to be integers that satisfy the inequalities -4 <= x =<5 and 6=<y =<16. How many different triangles with these properties could be constructed? (A) 110 (B) 1,100 (0 9,900 (D) 10,000 (E) 12,100

Merging topics. Please refer to the solutions above.