A right triangle ABC has to be constructed in the xy-plane : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 10:03

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A right triangle ABC has to be constructed in the xy-plane

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Sep 2009
Posts: 41
Followers: 0

Kudos [?]: 80 [7] , given: 4

A right triangle ABC has to be constructed in the xy-plane [#permalink]

### Show Tags

22 May 2010, 14:05
7
KUDOS
25
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (02:20) correct 21% (02:05) wrong based on 403 sessions

### HideShow timer Statistics

A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

A. 100
B. 6480
C. 2320
D. 1500
E. 9000

my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER
[Reveal] Spoiler: OA
Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 330
Followers: 14

Kudos [?]: 707 [0], given: 28

### Show Tags

22 May 2010, 20:54
shekar123 wrote:

A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER

You are going in the right direction. For A there are 90 possibilities. However, for B we are bound by A, so we have only 8 possibilities because B has to have the same x-coordinate as A. Similarly C has 9 possibilities.
Total: 90*8*10= 7200
_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Manager
Joined: 16 Mar 2010
Posts: 184
Followers: 3

Kudos [?]: 176 [2] , given: 9

### Show Tags

23 May 2010, 04:48
2
KUDOS
1
This post was
BOOKMARKED
Friends,
I am trying to provide my thinking below:
For A, there are 90 possibilities on the plane.
For each location of A, as the triangle has to have same properties, there are 8 possibilities on the x axis and 9 possibilities on y axis.
So the answer is 90*8*9 = 6480

Consider giving me KUDOS if you find my post useful.
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7091

Kudos [?]: 93343 [0], given: 10557

### Show Tags

23 May 2010, 05:06
Expert's post
7
This post was
BOOKMARKED
shekar123 wrote:

A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

my analysis

A(x,y) - 9,10- 90 possible values
B(x,y) - 8,10 =80 possible values
C(X,Y) -9,9 =81 POBBILE VALUES

i DON'T KNOW HOW TO PROCEED LATER

amitjash's solution is correct.

We have the rectangle with dimensions 9*10 (9 horizontal dots and 10 vertical). AB is parallel to x-axis and AC is parallel to y-axis.

Choose the (x,y) coordinates for vertex A: 9C1*10C1=90;
Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex C (as x coordinate is fixed by A): 9C1, (10-1=9 as 1 vertical dot is already occupied by A).

9C1*10C1*8C1*9C1=6480.

_________________
Retired Moderator
Joined: 03 Aug 2010
Posts: 246
Followers: 2

Kudos [?]: 37 [0], given: 41

### Show Tags

21 Dec 2010, 08:10
A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

100
6480
2320
1500
9000
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7091

Kudos [?]: 93343 [1] , given: 10557

### Show Tags

21 Dec 2010, 08:15
1
KUDOS
Expert's post
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 240 [0], given: 10

### Show Tags

15 Jun 2011, 23:41
A 9*10 for x and y.

B 8* 1

C 1* 9
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13484
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

### Show Tags

11 Jan 2014, 03:43
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.
_________________
Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 157
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 1

Kudos [?]: 85 [1] , given: 39

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

### Show Tags

30 Jul 2014, 05:55
1
KUDOS
[quote="shekar123"]A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?

A. 100
B. 6480
C. 2320
D. 1500
E. 9000

Sol:

let's find point A first:
X- axis_ point A :: point A can be any where between -3 and 5 on X- axis (total point = 5-(-3)+1 = 9)= 9c1
Y- axis_ point A :: for each x-coordinate the point A can take any value from 2 to 11 (11-2+1) in Y -coordinate= 10c1

A : 9c1*10c1

Lets Now find point B :

X- axis _ Point B:: from remaining X cordinates( A has already taken one), B can take any value so 8C1
Y - axis_point B :: No bother because it will be on same co-ordinate as A

B: 8C1

Now point C:
X: It has to be alias with A so no bother
Y: It can take any value from remaining 9 (one already taken by A) , 9C1

total: 9c1*10c1*8c1*9c1 = 6480 !!!!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13484
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

### Show Tags

19 Sep 2015, 22:06
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 Club Legend
Joined: 09 Sep 2013
Posts: 13484
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: A right triangle ABC has to be constructed in the xy-plane [#permalink]

### Show Tags

29 Sep 2016, 14:15
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.
_________________
Re: A right triangle ABC has to be constructed in the xy-plane   [#permalink] 29 Sep 2016, 14:15
Similar topics Replies Last post
Similar
Topics:
15 Right triangle RST can be constructed in the xy-plane such 6 10 Aug 2012, 22:28
20 Triangle ABC will be constructed in a xy-plane according to 3 14 May 2012, 14:32
44 A right triangle ABC has to be constructed in the xy-plane 9 08 Sep 2010, 11:21
92 Right triangle PQR is to be constructed in the xy-plane so 23 23 Dec 2009, 19:52
162 Right triangle PQR is to be constructed in the xy-plane so 17 13 Oct 2008, 02:13
Display posts from previous: Sort by