Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2016, 14:45
GMAT Club Tests

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Right triangle RST can be constructed in the xy-plane such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 26 Jun 2012
Posts: 1
Followers: 0

Kudos [?]: 3 [1] , given: 0

GMAT ToolKit User Premium Member
Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 10 Aug 2012, 23:28
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (02:22) correct 57% (01:40) wrong based on 185 sessions

HideShow timer Statistics

Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R. The x and y-coordinates of R, S, and T are to be nonzero integers that satisfy the inequalities −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3. Given these restrictions, how many different triangles can be constructed?

A. 3780
B. 4200
C. 4900
D. 6160
E. 7744
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Aug 2012, 00:19, edited 1 time in total.
Edited the question.
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33997
Followers: 6075

Kudos [?]: 76249 [2] , given: 9969

Re: Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 11 Aug 2012, 00:34
2
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
toshreyansjain wrote:
Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R. The x and y-coordinates of R, S, and T are to be nonzero integers that satisfy the inequalities −3 ≤ x ≤ 4 and −7 ≤ y ≤ 3. Given these restrictions, how many different triangles can be constructed?

A. 3780
B. 4200
C. 4900
D. 6160
E. 7744


−3 ≤ x ≤ 4 and −7 ≤ y ≤ 3 gives a rectangle with 8*11 dimensions (8 horizontal and 11 vertical dots). We are given that RS is parallel to x-axis, RT is parallel to y-axis and the right angle is at R.

Choose the (x,y) coordinates for vertex R: 7C1*10C1 (we are told that coordinates of R, S, and T must be nonzero integers, so we are choosing from 7 and 10 instead of 8 and 11 because we should exclude 0);

Choose the x coordinate for vertex S (as y coordinate is fixed by R): 6C1, (7-1=6 as 1 horizontal dot is already occupied by R);

Choose the y coordinate for vertex T (as x coordinate is fixed by R): 9C1, (10-1=9 as 1 vertical dot is already occupied by B).

7C1*10C1*6C1*9C1=3,780.

Answer: A.

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-71597.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

Also, please read and follow: 11-rules-for-posting-133935.html (rule #3)
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 3255
Followers: 1089

Kudos [?]: 4764 [0], given: 53

Re: Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 09 Sep 2013, 14:03
Expert's post
judokan 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 < or= x < or = 5 and 6 < or= y < or = 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

kanusha wrote:
sir, in the below steps i did not understand what is x coordinate for vertex R and Q? what is mean by coordinate is fixed by A?? How and why values 9c1 and 10c1 are used??

We have the rectangle with dimensions 10*11 (10 horizontal dots and 11 vertical). RT is parallel to y-axis and RS is parallel to x-axis.
Choose the (x,y) coordinates for vertex R (right angle): 10C1*11C1;
Choose the x coordinate for vertex S (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 T (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.

though it might be silly doubt.. pls send if their is any concept that i lack understand this problem.
pls reply, thank you.

Dear kanusha,

I'm happy to help. :-)

This question requires a little visualization and some facility with the x-y plane. The question tells us "Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R." This tells us
(a) there is a right angle at R, so RS is perpendicular to RT
(b) RS is parallel to the x-axis, perpendicular to the y-axis --- i.e. horizontal
(c) RT must be parallel to the y-axis, perpendicular to the x-axis --- i.e. vertical

Then, we have to recognize --- all points on the same horizontal line have the same height, so they all have the same y-coordinate. Therefore, we absolutely know that R & S, endpoints of the horizontal line, must have the same x-coordinate.

Similarly ---- all points on any vertical line share the same distance from the y-axis, the same length to the right or the left of the y-axis, so all points on the same vertical line must have the same x-coordinate. Thus, R & T, the endpoints of a vertical line, have the same y-coordinate.

Next, inclusive counting. See
http://magoosh.com/gmat/2012/inclusive- ... -the-gmat/
From x = -4 to x = +5, there are (+5) - (-4) + 1 = 10 points, and, similarly, 11 possible y-points.

Does this clear up your question? On precisely which part do you have questions?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Manager
Manager
avatar
Joined: 23 May 2013
Posts: 132
Concentration: Strategy, Social Entrepreneurship
GMAT Date: 08-05-2015
Followers: 1

Kudos [?]: 48 [0], given: 38

GMAT ToolKit User CAT Tests
Re: Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 09 Jun 2014, 10:18
Tricky Question!

Imagine we have a grid, ranging from -3 to 7 on the x-axis, and from -7 to 3 on the y-axis. Every point on this grid could potentially be point R, the right angle of the triangle (EXCEPT ANY POINT ON THE AXES - the question says *non-zero* integers! They're not talking about the length of the side, they mean the coordinates of the points. This is very important!). Thus, we're left with 7*10 = 70 choices for our point R.

Now we know that the sides of the triangle are parallel with the axes, so the other points must lie on the same horizontal or vertical as our point R. Therefore, we have 7-1 = 6 choices for the one on the x axis, and 10-1= 9 choices for the one on the y-axis (we subtract one from each because we can't have the same point).

Therefore, in total, we have 7*10*6*9 = 54*70 = 3500 + 280 = 3780 possible choices.

Answer: A

Notice if they had NOT stated that the coordinates had to be non zero, we would have had 8*11 choices for R, and 7 and 10 choices for the other points, respectively. The number of possibilities here is 8*11*7*10 = 88*70 = 5600+560 = 6160, answer D. Very tricky!
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10563
Followers: 495

Kudos [?]: 129 [0], given: 0

Premium Member
Re: Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 03 Jun 2016, 19:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 21 Sep 2015
Posts: 68
Location: India
GMAT 1: 730 Q48 V42
Followers: 1

Kudos [?]: 13 [0], given: 252

Reviews Badge CAT Tests
Right triangle RST can be constructed in the xy-plane such [#permalink]

Show Tags

New post 16 Jun 2016, 00:00
No of ways of choosing R(x,y) = 10*7
No of ways of choosing S =1*6
no of ways of choosing T= 9*1

Therefore total number of ways = 10* 7 *9 *6
=3780
Attachments

solution.png
solution.png [ 7.75 KiB | Viewed 252 times ]


_________________

Appreciate any KUDOS given ! :)

Right triangle RST can be constructed in the xy-plane such   [#permalink] 16 Jun 2016, 00:00
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Right triangle RST can be constructed in the xy-plane such satsymbol 2 17 Aug 2014, 23:35
28 Experts publish their posts in the topic A right triangle ABC has to be constructed in the xy-plane shekar123 9 22 May 2010, 15:05
64 Experts publish their posts in the topic Right triangle PQR is to be constructed in the xy-plane so gmatJP 21 23 Dec 2009, 20:52
124 Experts publish their posts in the topic Right triangle PQR is to be constructed in the xy-plane so amitdgr 12 13 Oct 2008, 03:13
10 Experts publish their posts in the topic Right triangle PQR is to be constructed in the xy-plane so haas_mba07 18 07 Aug 2006, 18:31
Display posts from previous: Sort by

Right triangle RST can be constructed in the xy-plane such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.