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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
There's always a better way." This critical mantra can save clever students untold struggle on the GMAT Quantitative section. Let's examine some challenging questions that reward students who possess the mental flexibility to shift perspective.
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days.
A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
22 May 2010, 14:05
9
74
00:00
A
B
C
D
E
Difficulty:
35% (medium)
Question Stats:
71% (01:59) correct 29% (02:44) wrong based on 453 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?
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
23 May 2010, 05:06
8
10
shekar123 wrote:
Please help me with this question
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).
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
22 May 2010, 20:54
shekar123 wrote:
Please help me with this question
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
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
23 May 2010, 04:48
2
1
Friends, Please provide the OA. 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 Please provide the OA.
Consider giving me KUDOS if you find my post useful.
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
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?
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
30 Jul 2014, 05:55
3
[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
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
10 Feb 2019, 22:36
1
Solution: Let’s draw a diagram to analyze the question:
Attachment:
image1.PNG [ 17.14 KiB | Viewed 2380 times ]
Right angled triangle ABC, right angled at A, satisfying the following conditions: -3 ≤x1, x2≤ 5 and 2 ≤y1, y2≤ 11 Let the x and y coordinates for vertex A = (x1 and y1) Let the x and y coordinates for vertex B = (x1 and y2) [As AB is parallel to Y Axis, “x” coordinate will be same as the vertex A only “Y” coordinate will change.] Let the x and y coordinates for vertex C = (x2 and y1) [As AC is parallel to X Axis, “y” coordinate will be same as the vertex A only “X” coordinate will change.] So, as the diagram represents the number of triangles with the given conditions will vary as x1 and x2’s and y1 and y2’s vary. The total number of possibilities of triangles = x1 ×x2 ×y1 ×y2 = 9C1 8C1 10C1 9C1 = 6480 The correct answer option is “B”
_________________
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
14 Mar 2019, 21:04
Bunuel wrote:
shekar123 wrote:
Please help me with this question
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.
Answer: B.
hi sir , i do understand all the algebra and combinations leading to the answer , but while selecting points don't we have to consider the validity of pythagoras theorem ? , such that the selected coordinates satisfy it as it is a right triangle , as our selection criteria seems to be based on just selecting points
Re: A right triangle ABC has to be constructed in the xy-plane so that the
[#permalink]
Show Tags
24 Mar 2020, 05:58
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.
_________________
close
71% (01:59) correct 
