It is currently 21 Sep 2020, 12:14
My 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.

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Active Member
Active Member
User avatar
Joined: 07 Jan 2018
Posts: 694
Followers: 11

Kudos [?]: 769 [1] , given: 88

If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 08 May 2018, 04:00
1
This post received
KUDOS
00:00

Question Stats:

58% (02:36) correct 42% (01:29) wrong based on 50 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


src: Brightlink Prep
[Reveal] Spoiler: OA
3 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 3827
Followers: 148

Kudos [?]: 4472 [3] , given: 69

CAT Tests
Re: If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 08 May 2018, 07:07
3
This post received
KUDOS
Expert's post
amorphous 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


There are two ways to create these triangles:
1) select 2 points from the first line (the line with 4 points) and select 1 point from the second line (the line with 5 points)
2) select 1 point from the first line (the line with 4 points) and select 2 points from the second line (the line with 5 points)


Once we have selected 3 points, we simply connect them with lines to form a triangle

We'll handle each option separately.

----------------------------------------
1) select 2 points from the first line (the line with 4 points) and select 1 point from the second line (the line with 5 points)
Take the task of selecting points and break it into stages.

Stage 1: Select two points from the first line
Since the order in which we select the points does not matter, we can use combinations.
We can select 2 points from 4 points in 4C2 ways (6 ways)
So, we can complete stage 1 in 6 ways

Stage 2: Select one point from the second line
There are 5 points to choose from, so we can complete this stage in 5 ways.

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create triangles) in (6)(5) ways (= 30 ways)
----------------------------------------

2) select 1 point from the first line (the line with 4 points) and select 2 points from the second line (the line with 5 points)
Stage 1: Select one point from the first line
There are 4 points to choose from, so we can complete this stage in 4 ways.

Stage 2: Select two point from the second line
Since the order in which we select the points does not matter, we can use combinations.
We can select 2 points from 5 points in 5C2 ways (10 ways)
So, we can complete stage 2 in 10 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create triangles) in (4)(10) ways (= 40 ways)
--------------------------------------------

TOTAL number of triangles = 30 + 40 = 70

Answer: D

RELATED VIDEOS FROM OUR COURSE



_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
Image
Sign up for GRE Question of the Day emails

Intern
Intern
Joined: 26 Apr 2019
Posts: 1
Followers: 0

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

Re: If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 16 Jun 2019, 04:22
What about just doing 5C2 and then 4C2 then adding the results together to get 70?
Manager
Manager
Joined: 22 Aug 2019
Posts: 72
Followers: 1

Kudos [?]: 51 [0], given: 11

Re: If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 22 Aug 2019, 17:20
hmasters1993 wrote:
What about just doing 5C2 and then 4C2 then adding the results together to get 70?


I think that equals 16?
1 KUDOS received
VP
VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1309 [1] , given: 251

Re: If 4 points are indicated on a line and 5 points are indicat [#permalink] New post 23 Aug 2019, 05:16
1
This post received
KUDOS
hmasters1993 wrote:
What about just doing 5C2 and then 4C2 then adding the results together to get 70?



Kindly, refer to the below diag.

CASE 1:

First line, there are 4 points

2 nd line, there are 5 points.

Now to make a triangle we need 3 POINTS.

First let us take 1 point from 1st line and 2 points from the second line

Since first line as 4 points and we need only 1, hence we choose in 4C1 = 4 ways

Next in the second line, there are 5 points and we need 2 points, hence we can choose in 5C2 = 10 ways

Therefore for CASE 1 ; total no. of ways = 4 * 10 = 40


CASE 2 :

First line, there are 4 points

2 nd line, there are 5 points.

Now to make a triangle we need 3 POINTS.

First let us take 2 points from 1st line and 1 point from the second line

Since first line as 4 points and we need only 2, hence we choose in 4C2 = 6 ways

Next in the second line, there are 5 points and we need 1 point, hence we can choose in 5C1 = 5 ways

Therefore for CASE 2 ; total no. of ways = 6 * 5 = 30 ways

Total no. of ways taking all possibility = 40 + 30 = 70 ways
Attachments

FIGURE.jpg
FIGURE.jpg [ 36.22 KiB | Viewed 1114 times ]


_________________

If you found this post useful, please let me know by pressing the Kudos Button


Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Re: If 4 points are indicated on a line and 5 points are indicat   [#permalink] 23 Aug 2019, 05:16
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.