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

It is currently 20 Oct 2014, 00:29

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

If 4 points are indicated on a line and 5 points are

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 41 [1] , given: 117

If 4 points are indicated on a line and 5 points are [#permalink] New post 16 May 2012, 05:52
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:58) correct 23% (00:36) wrong based on 153 sessions
If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

A. 20
B. 30
C. 40
D. 70
E. 90

Tried doing a few options, but couldn't get it right and the answer provided left me more confused!
[Reveal] Spoiler: OA
3 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 13 May 2011
Posts: 324
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 19

Kudos [?]: 136 [3] , given: 11

Re: If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 16 May 2012, 06:04
3
This post received
KUDOS
say line A with 4 points and line B with 5 points. and triangle is PQR.
If P is on line A and QR on line B we can have 4C1*5C2=40 triangles.
If P is on line B and QR on line A we can have 4C2*5C1=30 triangles.
Total =70 triangles.
Expert Post
13 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23324
Followers: 3599

Kudos [?]: 28585 [13] , given: 2803

Re: If 4 points are indicated on a line and 5 points are [#permalink] New post 16 May 2012, 06:58
13
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
alexpavlos wrote:
If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

A. 20
B. 30
C. 40
D. 70
E. 90

Tried doing a few options, but couldn't get it right and the answer provided left me more confused!


Approach #1:
There are two types of triangles possible:
With two vertices on the line with 4 points and the third vertex on the line with 5 points --> C^2_4*C^1_5=30;
With two vertices on the line with 5 points and the third vertex on the line with 4 points --> C^2_5*C^1_4=40;

Total: 30+40=70.

Answer: D.

Approach #2:

All different 3 points out of total 4+5=9 points will create a triangle EXCEPT those 3 points which are collinear.
C^3_{9}-(C^3_4+C^3_5)=84-(4+10)=70 (where C^3_4 and C^3_4 are # of different 3 collinear points possible from the line with 4 points and the line with 5 points, respectively).

Answer: D.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 16

Kudos [?]: 202 [1] , given: 11

GMAT ToolKit User
Re: If 4 points are indicated on a line and 5 points are [#permalink] New post 29 Dec 2012, 00:27
1
This post received
KUDOS
Not that fun this question :( I wonder how often I would see such a question on test day.

Solution:

* * * * * (line B)

* * * * (line A)

Choose 2 points from line A and a point from line B: = 4!/2!2! * 5!/1!4! = 30
Choose 1 point from line A and 2 points from line B: = 4!/1!3! * 5!/2!3! = 4 * 10 = 40

Combine possiblities: 30 + 40 = 70
_________________

Impossible is nothing to God.

Intern
Intern
avatar
Joined: 10 Apr 2012
Posts: 23
Concentration: Finance, Economics
GMAT 1: 700 Q47 V38
GMAT 2: 650 Q45 V35
GMAT 3: 760 Q50 V44
Followers: 0

Kudos [?]: 21 [0], given: 0

Re: If 4 points are indicated on a line and 5 points are [#permalink] New post 19 Jul 2014, 20:45
See Image below for what my scratch paper looked like on this one
Attachments

Gmat_56_resized.jpg
Gmat_56_resized.jpg [ 101.22 KiB | Viewed 728 times ]

Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 229
Followers: 5

Kudos [?]: 45 [0], given: 138

GMAT ToolKit User CAT Tests
Re: If 4 points are indicated on a line and 5 points are [#permalink] New post 19 Jul 2014, 21:47
Bunuel wrote:
alexpavlos wrote:
If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

A. 20
B. 30
C. 40
D. 70
E. 90

Tried doing a few options, but couldn't get it right and the answer provided left me more confused!


Approach #1:
There are two types of triangles possible:
With two vertices on the line with 4 points and the third vertex on the line with 5 points --> C^2_4*C^1_5=30;
With two vertices on the line with 5 points and the third vertex on the line with 4 points --> C^2_5*C^1_4=40;

Total: 30+40=70.

Answer: D.

Approach #2:

All different 3 points out of total 4+5=9 points will create a triangle EXCEPT those 3 points which are collinear.
C^3_{9}-(C^3_4+C^3_5)=84-(4+10)=70 (where C^3_4 and C^3_4 are # of different 3 collinear points possible from the line with 4 points and the line with 5 points, respectively).

Answer: D.

Hope it's clear.


I really like your 2nd approach :-D
_________________

.........................................................................
+1 Kudos please, if you like my post

Re: If 4 points are indicated on a line and 5 points are   [#permalink] 19 Jul 2014, 21:47
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If the point (4,6) lies on line l, and the point (x,3) gauravsoni 5 20 May 2014, 11:32
Points on a line enigma123 0 14 Dec 2011, 05:43
On the number line, the distance between point A and C is 5 alimad 3 27 Jun 2008, 14:45
On the number line the distance between point A and C is 5 bewakoof 5 22 Jul 2007, 20:28
Which point is symmetric with point (-5,-2) about the line Ethan 2 28 Mar 2006, 07:18
Display posts from previous: Sort by

If 4 points are indicated on a line and 5 points are

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.