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  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

     December 14, 2018

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Geometry

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Geometry  [#permalink]

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New post Updated on: 07 Aug 2018, 10:30
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A
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E

Difficulty:

  65% (hard)

Question Stats:

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

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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

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.
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Re: Geometry  [#permalink]

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New post 07 Aug 2018, 09:04
sadd 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..
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Re: Geometry  [#permalink]

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New post 07 Aug 2018, 09:14
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Top Contributor
GMAT215 wrote:
sadd 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)

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Brent
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Re: Geometry  [#permalink]

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New post 07 Aug 2018, 09:55
1
sadd 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?


\(@sadd\) -

Whats the OA for this? Is it A?
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Re: Geometry  [#permalink]

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New post 07 Aug 2018, 10:03
sadd 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?


IMO C

Can you please provide the OA please ?
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Re: Geometry  [#permalink]

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New post 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

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Geometry  [#permalink]

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New post 07 Aug 2018, 10:42
1
sadd 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?


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
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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Re: Geometry  [#permalink]

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New post 08 Aug 2018, 02:08
sadd 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?


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

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Re: Geometry &nbs [#permalink] 08 Aug 2018, 02:08
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