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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

1st line - 0 points
2nd line - new 1 point
3td line - new 2 points + old 1 point
4th line - new 3 points + old 2+1 points
5th line - new 4 points + old 3+2+1 points
n-th line - (n-1) points + (n-2) .... 3+2+1

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300 B 600 C 250 D 300 E none of these

Soln: Since no three are concurrent, hence any point that is formed by two different lines are distinct. The first line intersects each of the other 24 lines at 24 points. => statement 1 The second line intersects each of the other 23 lines at 23 points. The point with first line has already been counted in the statement no.1. The third line intersects each of the other 22 lines at 22 points and so on.

Thus total number of points is = 24 + 23 + 22 + ... + 1 = 24 * 25/2 = 300

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300 B 600 C 250 D 300 E none of these

Please explaing for me to understand the concept

Amar

No three lines are concurrent and no two lines are parallel gives us the info that every line intersects the other and no intersection point is common. Hence no of intersection points = 25c2 = 300 = D _________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300 B 600 C 250 D 300 E none of these

Please explaing for me to understand the concept

Amar

Responding to a pm:

We need to draw lines such that they are not parallel. Why is 'not parallel' important? Any two distinct lines drawn on the xy axis will either be parallel or will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. Since any given two lines are not parallel, we can say that they must intersect at exactly one point. So every pair of two lines will intersect at exactly one point. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line. So how many such unique points of intersection do we get? That depends on how many pairs of 2 lines can we select from the 25 lines? We can select 2 lines from 25 lines in 25C2 ways i.e. 300 ways. Each one of these pairs will give us one unique point of intersection so we will get 300 points of intersection.

Re: If 25 lines are drawn in a plane such that no two of them [#permalink]

Show Tags

12 Dec 2013, 23:28

The answer is easier than it seems to be 25C2=300 As any two lines have exactly 1 intersection point (just draw a few non-parallel lines), we simply need to find in how many ways we can chose 2 lines out of 25

Re: If 25 lines are drawn in a plane such that no two of them [#permalink]

Show Tags

26 Feb 2014, 17:26

Amardeep Sharma wrote:

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A. 2300 B. 600 C. 250 D. 300 E. none of these

No 3 lines intersect at one point.. and none of them are parallel... point is created when 2 lines intersect... how many ways can you select 2 out of 25 = 25C2=300

Re: If 25 lines are drawn in a plane such that no two of them [#permalink]

Show Tags

26 Apr 2015, 15:17

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. _________________

READ:http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html Classroom Centre Address: GMATinsight 107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075 ______________________________________________________ Please press the if you appreciate this post !!

Re: If 25 lines are drawn in a plane such that no two of them [#permalink]

Show Tags

13 Aug 2016, 10:39

Amardeep Sharma wrote:

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A. 2300 B. 600 C. 250 D. 300 E. none of these

Answer is n(n-1)/2 Just remember a simple thing, same concept applies to handshakes, no. of matches in tournament. nC2 is the answer. Hence (25X24)/2=300 D _________________

Re: If 25 lines are drawn in a plane such that no two of them [#permalink]

Show Tags

18 Aug 2016, 21:23

Amardeep Sharma wrote:

If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A. 2300 B. 600 C. 250 D. 300 E. none of these

The keywords are "no two of them are parallel" and "no three are concurrent". The former meaning, given any two lines, they intersect at only point and the latter meaning at any intersection points, it's only 2 lines that are intersecting and not more than that. This is to ensure that every point of intersection is only between 2 lines.

So 1 pair of lines (2 lines) intersect at 1 point 3 lines intersect at 3 point , i.e, from 3 choose as a pair(2) , i.e 3C2 =3 4 lines intersect at, from 4 choose as a pair(2) = 4C2 = 6

So from 25 lines, choose in pairs = 25 C 2 = 25*24/2 = 300

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...