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:

Line L and line K have slopes -2 and 1/2 respectively. If line L and l [#permalink]

Show Tags

14 Sep 2015, 16:32

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

62% (01:42) correct
38% (01:40) wrong based on 147 sessions

HideShow timer Statistics

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K?

A) 5 B) 10 C) \(5\sqrt{5}\) D) 15 E) \(10\sqrt{5}\)

Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l [#permalink]

Show Tags

14 Sep 2015, 18:11

1

This post received KUDOS

skylimit wrote:

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K? A) 5 B) 10 C) \(5\sqrt{5}\) D) 15 E)\(10\sqrt{5}\)

Source: GMAT Prep Now

Is there a nice fast solution?

Follow the posting guidelines.

As for your question, "Is there a nice fast solution?", it is not going to be helpful either to you or any other member when you ask such questions without providing information as to what did you do to approach this question. It is fine to ask an "alternate method" but to talk about "fastest" or "easiest" is going to defeat the purpose of having a useful discussion.

The classic way is:

Assume the equations of the 2 lines, L and K as

y=-2x+a and y=x/2 +b respectively

As both these lines pass through (6,8), substitute x=6 and y=8 to get the values of a and b as 20 and 5 respectively.

Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l [#permalink]

Show Tags

15 Sep 2015, 07:12

Engr2012 wrote:

As for your question, "Is there a nice fast solution?", it is not going to be helpful either to you or any other member when you ask such questions without providing information as to what did you do to approach this question. It is fine to ask an "alternate method" but to talk about "fastest" or "easiest" is going to defeat the purpose of having a useful discussion.

I agree. However, the site doesn't allow links in posts for first 5 days and this makes it hard. I didn't know how to solve the question. When I checked the video solution I thought it was too long of an approach. So, I asked for a shorter solution. I guess I could have entered the complete solution from the video, but that seemed like a waste.

Thanks for your solution though. It's basically the same as the one in the video

Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l [#permalink]

Show Tags

15 Sep 2015, 07:19

skylimit wrote:

Engr2012 wrote:

As for your question, "Is there a nice fast solution?", it is not going to be helpful either to you or any other member when you ask such questions without providing information as to what did you do to approach this question. It is fine to ask an "alternate method" but to talk about "fastest" or "easiest" is going to defeat the purpose of having a useful discussion.

I agree. However, the site doesn't allow links in posts for first 5 days and this makes it hard. I didn't know how to solve the question. When I checked the video solution I thought it was too long of an approach. So, I asked for a shorter solution. I guess I could have entered the complete solution from the video, but that seemed like a waste.

Thanks for your solution though. It's basically the same as the one in the video

The solution above is per the basics of coordinate geometry and lines and took me all of 1.2 minute to solve this question. How much more quickly do you want to solve such a question? This question seems to be 650-700 level (more so towards 700) and thus would need you to apply a number of connected concepts in a particular form. I do believe that a graphical method would have been more straightforward (not quicker!) had the question asked for the area of the triangle formed by the 2 lines and the X-axis.
_________________

Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l [#permalink]

Show Tags

20 Apr 2016, 19:45

1

This post received KUDOS

skylimit wrote:

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K?

A) 5 B) 10 C) \(5\sqrt{5}\) D) 15 E) \(10\sqrt{5}\)

Source: GMAT Prep Now

my approach: plug in values for each equation y=-2x+b => 8=-2*6 +b -> b=20 y=x/2+b => 8=6/2 +b => b=5 (Y INTERCEPT OF THE LINE K)

now, let's find for x intercept of line L. y must be zero 0=-2x+20 -> x=10

so we have a right triangle with leg 5 and 10. the distance between these two points is: sqrt(5^2 + 10^2) = sqrt(125) = 5*sqrt(5)

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K?

A) 5 B) 10 C) \(5\sqrt{5}\) D) 15 E) \(10\sqrt{5}\)

Source: GMAT Prep Now

You can also use the concept of slope.

Slope = -2 means that for every 1 unit increase in x co-ordinate, y co-ordinate decreases by 2. Line L has slope -2 and passes through (6, 8). It's x intercept will have y = 0 i.e. a decrease of 8 so x will increase by 4 to 6 + 4 = 10. So x intercept is 10.

Line K has slope 1/2 and passes through (6, 8). It's y intercept will have x = 0 i.e. a decrease of 6 so y will decrease by 1/2 of that i.e. by 3. So y intercept is 8 - 3 = 5.

Distance between the two points can be found using pythagorean theorem as \(\sqrt{10^2 + 5^2} = 5\sqrt{5}\).

Line l and k have slope -2 and 1/2 respectively. if line l and k inter [#permalink]

Show Tags

30 Apr 2017, 06:37

Line l and k have slope -2 and 1/2 respectively. if line l and k intersect at (6 , 8). What is the distance between the x intercept of line l and the y intercept of line k?

Line l and k have slope -2 and 1/2 respectively. if line l and k intersect at (6 , 8). What is the distance between the x intercept of line l and the y intercept of line k?

A) 5

B) 10

C) 5 \sqrt{}5

D)15

E) 10\sqrt{5}

Merging topics. Please refer to the discussion above.
_________________