• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for \$49 worth of Veritas practice GMATs FREE

VERITAS PRACTICE GMAT EXAMS
Earn 10 Points Per Post
Earn 10 Points Per Thanks
Earn 10 Points Per Upvote

## another tough OG question

##### This topic has expert replies
Legendary Member
Posts: 512
Joined: 18 Jun 2012
Thanked: 42 times
Followed by:19 members

### another tough OG question

by sana.noor » Fri Apr 19, 2013 6:31 am
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 â‰¤ x â‰¤ 5 and 6 â‰¤ y â‰¤ 16. How many different triangles with these properties can be constructed?
(A) 110
(B) 1100
(C) 9900
(D) 10000
(E) 12100

C
Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button.

### GMAT/MBA Expert

GMAT Instructor
Posts: 14220
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1259 members
GMAT Score:770
by Brent@GMATPrepNow » Fri Apr 19, 2013 6:34 am
sana.noor 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 â‰¤ x â‰¤ 5 and 6 â‰¤ y â‰¤ 16. How many different triangles with these properties can be constructed?
(A) 110
(B) 1100
(C) 9900
(D) 10000
(E) 12100

C
Take the task of building triangles and break it into stages.

Stage 1: Select any point where the right angle will be (point P).
The point can be selected from a 10x11 grid. So, there 110 points to choose from.
This means that stage 1 can be completed in 110 ways.

Stage 2: Select a point that is on the same horizontal line as the first point. This point will be point R.
The 2 legs of the right triangle are parallel to the x- and y-axes.
The first point we select (in stage 1) dictates the y-coordinate of point R.
In how many ways can we select the x-coordinate of point R?
Well, we can choose any of the 10 coordinates from -4 to 5 inclusive EXCEPT for the x-coordinate we chose for point P (in stage 1).
So, there are 9 coordinates to choose from.
This means that stage 2 can be completed in 9 ways.

Stage 3: Select a point that is on the same vertical line as the first point. This point will be point Q.
The 2 legs of the right triangle are parallel to the x- and y-axes.
The first point we select (in stage 1) dictates the x-coordinate of point Q.
In how many ways can we select the y-coordinate of point Q?
Well, we can choose any of the 11 coordinates from 6 to 16 inclusive EXCEPT for the y-coordinate we chose for point P (in stage 1).
So, there are 10 coordinates to choose from.
This means that stage 3 can be completed in 10 ways.

So, by the Fundamental Counting Principle (FCP), the total number of triangles = (110)(9)(10) = [spoiler]9900 = C[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Watch these video reviews of my course
And check out these free resources

### GMAT/MBA Expert

GMAT Instructor
Posts: 14220
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1259 members
GMAT Score:770
by Brent@GMATPrepNow » Fri Apr 19, 2013 6:37 am
If you're interested, here's another 700+ level question involving counting triangles in the coordinate plane: https://www.beatthegmat.com/how-many-tri ... 28974.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Watch these video reviews of my course
And check out these free resources

### GMAT/MBA Expert

GMAT Instructor
Posts: 511
Joined: 11 Aug 2010
Location: Delhi, India
Thanked: 344 times
Followed by:86 members
by Anju@Gurome » Fri Apr 19, 2013 7:00 am
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

Â§ GMAT with Gurome Â§ Admissions with Gurome Â§ Career Advising with Gurome Â§

GMAT Instructor
Posts: 15497
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1886 members
GMAT Score:790
by GMATGuruNY » Fri Apr 19, 2013 7:24 am
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.