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# Geometry

Author Message
Intern
Joined: 21 Jul 2018
Posts: 1

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Updated on: 07 Aug 2018, 10:30
1
00:00

Difficulty:

65% (hard)

Question Stats:

50% (02:19) correct 50% (01:49) wrong based on 26 sessions

### HideShow timer Statistics

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

What is the right choice?

Originally posted by sadd on 07 Aug 2018, 08:41.
Last edited by sadd on 07 Aug 2018, 10:30, edited 1 time in total.
Manager
Joined: 01 Feb 2018
Posts: 77
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 4
WE: Consulting (Consulting)

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07 Aug 2018, 09:04
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

What is the right choice?

can you pls mention source of this question..
CEO
Joined: 11 Sep 2015
Posts: 3237

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07 Aug 2018, 09:14
1
Top Contributor
GMAT215 wrote:
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

What is the right choice?

can you pls mention source of this question..

This is a question from an Official Guide (from many years ago)

Cheers,
Brent
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Director
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)

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07 Aug 2018, 09:55
1
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

What is the right choice?

$$@sadd$$ -

Whats the OA for this? Is it A?
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Manager
Joined: 11 Mar 2018
Posts: 90

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07 Aug 2018, 10:03
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

What is the right choice?

IMO C

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Intern
Joined: 10 Sep 2017
Posts: 10

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07 Aug 2018, 10:38
1
Let's fix a position for point P first,
It can have 10 ( x values) * 11 (y values) = 110 places.
point R can take 9 x values and similarly point Q can take 10 y values.
So total triangles can be
110*9*10= 9900

Posted from my mobile device
Senior Manager
Joined: 22 Feb 2018
Posts: 411

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07 Aug 2018, 10:42
1
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

What is the right choice?

OA: C
Given :$$-4 <= x <= 5;6<= y<= 16$$
As given PR is parallel to x axis

for $$y=6$$, We have $$10$$ $$(-4 <= x <= 5)$$ options for selecting $$R$$, Then $$9$$ ($$-4 <= x <= 5$$minus one,which is already selected for $$R$$) options available for selecting $$P$$ and for $$Q$$ we have $$10$$ ( $$6<= y<= 16$$ minus $$y=6$$ otherwise all $$3$$ point will be collinear)
Attachment:

triangle possibility.PNG [ 20.21 KiB | Viewed 376 times ]

Total triangle for $$y=6 : 9*10*10 =900 triangles$$
Similarily
for y $$=7 : 900$$ triangles
for y $$=8 : 900$$ triangles
.
.
.
.
for y $$=16 : 900$$ triangles

Total triangle $$= (16-6+1)*900 =9900$$
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Math Expert
Joined: 02 Sep 2009
Posts: 51215

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08 Aug 2018, 02:08
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

What is the right choice?

Discussed here: https://gmatclub.com/forum/right-triang ... 71597.html

THE TOPIC IS LOCKED AND ARCHIVED.
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Re: Geometry &nbs [#permalink] 08 Aug 2018, 02:08
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