It is currently 23 Oct 2017, 19:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Sep 2015
Posts: 26

Kudos [?]: 26 [0], given: 5

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

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) $$10\sqrt{5}$$

Source: GMAT Prep Now
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Sep 2015, 22:24, edited 2 times in total.
Edited the question.

Kudos [?]: 26 [0], given: 5

Current Student
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1731 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
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
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?

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.

Thus equations of the 2 lines become

L: y=-2x+20, x-intercept = (10,0) and
K: y=x/2 +5, y-intercept = (0,5) respectively

Thus the distance = distance between (10,0) and (0,5) = $$\sqrt {(10-0)^2+(0-5)^2}$$ = $$5\sqrt{5}$$. C is the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1731 [1], given: 792

Intern
Joined: 10 Sep 2015
Posts: 26

Kudos [?]: 26 [0], given: 5

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

Kudos [?]: 26 [0], given: 5

Current Student
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1731 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1731 [0], given: 792

CEO
Joined: 17 Jul 2014
Posts: 2605

Kudos [?]: 398 [1], given: 184

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
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
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)

C

Kudos [?]: 398 [1], given: 184

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7677

Kudos [?]: 17408 [1], given: 232

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

### Show Tags

21 Apr 2016, 02:20
1
KUDOS
Expert's post
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

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 $$\sqrt{10^2 + 5^2} = 5\sqrt{5}$$.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17408 [1], given: 232

Manager
Joined: 09 Jan 2016
Posts: 135

Kudos [?]: 88 [0], given: 59

GPA: 3.4
WE: General Management (Human Resources)
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?

A) 5

B) 10

C) 5 \sqrt{}5

D)15

E) 10\sqrt{5}

Kudos [?]: 88 [0], given: 59

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129537 [0], given: 12201

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

### Show Tags

30 Apr 2017, 07:05
Chemerical71 wrote:
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.
_________________

Kudos [?]: 129537 [0], given: 12201

Senior Manager
Joined: 29 Jun 2017
Posts: 347

Kudos [?]: 67 [1], given: 64

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

### Show Tags

23 Aug 2017, 07:24
1
KUDOS
Answer is clearly C as shown in figure.
Attachments

IMG_3955.JPG [ 1.67 MiB | Viewed 263 times ]

_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 67 [1], given: 64

Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l   [#permalink] 23 Aug 2017, 07:24
Display posts from previous: Sort by