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Intern  Joined: 10 Sep 2015
Posts: 26
Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 61% (02:35) correct 39% (02:27) wrong based on 219 sessions

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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

Originally posted by skylimit on 14 Sep 2015, 16:32.
Last edited by Bunuel on 14 Sep 2015, 22:24, edited 2 times in total.
Edited the question.
CEO  S
Joined: 20 Mar 2014
Posts: 2599
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]

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2
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.

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.
Intern  Joined: 10 Sep 2015
Posts: 26
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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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
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Schools: Kellogg '18 (M)
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Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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

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1
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
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Posts: 9705
Location: Pune, India
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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1
1
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 $$\sqrt{10^2 + 5^2} = 5\sqrt{5}$$.

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

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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}
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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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.
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Joined: 29 Jun 2017
Posts: 424
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Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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1
Answer is clearly C as shown in figure.
Attachments IMG_3955.JPG [ 1.67 MiB | Viewed 1111 times ]

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Intern  B
Joined: 06 Jul 2018
Posts: 2
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

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ENGRTOMBA2018 wrote:
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.

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.

In the above solution, you found the x-interecept of line L and y-interecept of line K. But if we do the opposite, i.e. find the x-int of line K and y-int of line L, the answer comes out to be different. why is that ? Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l   [#permalink] 07 Oct 2018, 02:58
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