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

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

Source : OG 11 (PS 248)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Mar 2012, 04:32, edited 1 time in total.
Edited the question and added the OA
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Re: PS : RIGHT TRIANGLE PQR [#permalink] New post 13 Oct 2008, 04:20
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Is it C?

P can take a total of 10*11 co-ordinates.
for a given P, R can take a total of 9 co-ordinates and Q can take a total of 10 co-ordinates.

Hence, total = 110*9*10 = 9900
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Re: PS : RIGHT TRIANGLE PQR [#permalink] New post 09 Dec 2010, 19:57
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.
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Re: PS : RIGHT TRIANGLE PQR [#permalink] New post 10 Dec 2010, 00:01
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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:
arithmetic-og-question-88380.html?hilit=constructed#p790651
geometry-and-combinations-100675.html?hilit=constructed#p777591
700-question-94644.html?hilit=constructed#p818546

Hope it helps.

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Re: PS : RIGHT TRIANGLE PQR [#permalink] New post 29 May 2011, 06:34
amitdgr wrote:
Source : OG 11 (PS 248)

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.

Ans: "C"

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Difficult Geometry Question [#permalink] New post 23 Aug 2011, 19:26
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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 is less than or equal to x which is less than or equal to 5 and 6 is less than or equal to y which is less than or equal to 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
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Re: Right triangle PQR is to be constructed in the xy-plane [#permalink] New post 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.

Similar questions to practice:
triangle-abc-will-be-constructed-in-a-xy-plane-according-to-132573.html
right-triangle-pqr-is-to-be-constructed-in-the-xy-plane-so-88380.html
right-triangle-abc-is-to-be-drawn-in-the-xy-plane-so-that-88958.html
a-right-triangle-abc-has-to-be-constructed-in-the-xy-plane-94644.html
a-right-triangle-abc-has-to-be-constructed-in-the-xy-plane-100675.html
right-triangle-rst-can-be-constructed-in-the-xy-plane-such-137129.html

All OG13 questions with solutions: the-official-guide-quantitative-question-directory-143450.html

Hope it helps.

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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Difficult Geometry Question [#permalink] New post 15 Jul 2014, 13:53
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Re: Difficult Geometry Question   [#permalink] 15 Jul 2014, 13:53
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