BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Tough one: Number of triangles

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 502
Joined: Tue Jun 03, 2008 11:36 pm
Thanked: 99 times
Followed by:21 members

Tough one: Number of triangles

by vk_vinayak » Mon Aug 27, 2012 12:53 am
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. 90
B. 900
C. 6480
D. 8100
E. 10000

OA Later.

[spoiler]Is it necessary to assume that co-ordinates are integers? It would be helpful if somebody explained how to tackle this within 2 minutes.[/spoiler]
- VK

I will (Learn. Recognize. Apply)
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 363
Joined: Sun Oct 17, 2010 3:24 pm
Thanked: 115 times
Followed by:3 members

by theCEO » Mon Aug 27, 2012 1:52 am
vk_vinayak 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?

A. 90
B. 900
C. 6480
D. 8100
E. 10000

OA Later.

[spoiler]Is it necessary to assume that co-ordinates are integers? It would be helpful if somebody explained how to tackle this within 2 minutes.[/spoiler]
[spoiler]ans = c[/spoiler]
Top
User avatar
Legendary Member
Posts: 502
Joined: Tue Jun 03, 2008 11:36 pm
Thanked: 99 times
Followed by:21 members

by vk_vinayak » Mon Aug 27, 2012 2:05 am
theCEO wrote:
vk_vinayak 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?

A. 90
B. 900
C. 6480
D. 8100
E. 10000

OA Later.

[spoiler]Is it necessary to assume that co-ordinates are integers? It would be helpful if somebody explained how to tackle this within 2 minutes.[/spoiler]
[spoiler]ans = c[/spoiler]
It would have been helpful if you provided the solution.
- VK

I will (Learn. Recognize. Apply)
Top
Senior | Next Rank: 100 Posts
Posts: 77
Joined: Tue Jul 31, 2012 6:53 am
Thanked: 8 times
Followed by:1 members

by GaneshMalkar » Mon Aug 27, 2012 2:47 am
theCEO wrote:
vk_vinayak 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?

A. 90
B. 900
C. 6480
D. 8100
E. 10000

OA Later.

[spoiler]Is it necessary to assume that co-ordinates are integers? It would be helpful if somebody explained how to tackle this within 2 minutes.[/spoiler]
[spoiler]ans = c[/spoiler]

Just trying to solve....It may not be right

As we have two inequalities which bound the area under consideration.
The two inequalities are -3 ≤ x ≤ 5 and 2 ≤ y ≤11 which makes a square of 9(parallel to x-axis) * 10(parallel to y axis).

1. So we need to have AB || to x axis
so A can take x coordinate from these 9 points in 9C1 ways and also can take from 10C1 points from the y coordinate...


2. Now as AB is parallel to x-axis
so B can take 8 such another points as 1 horizontal point is already occupied by A in 8C1 ways.

and C can take 9 such points as 1 point is took by A in 9C1 ways...

so total triangles drawn will be = 10C1 * 9C1 * 8C1 * 9C1 = 10 * 9 * 8 * 9 = 6480
If you cant explain it simply you dont understand it well enough!!!
- Genius
Top
Post new topic Post Reply
• Page 1 of 1