GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Dec 2018, 16:19

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

     December 14, 2018

     December 14, 2018

     10:00 PM PST

     11:00 PM PST

    Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

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

Show Tags

New post Updated on: 14 Sep 2015, 21:24
8
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

63% (01:46) correct 38% (01:55) wrong based on 208 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

Originally posted by skylimit on 14 Sep 2015, 15:32.
Last edited by Bunuel on 14 Sep 2015, 21:24, edited 2 times in total.
Edited the question.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 14 Sep 2015, 17:11
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
Intern
avatar
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]

Show Tags

New post 15 Sep 2015, 06:12
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
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 15 Sep 2015, 06:19
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.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2618
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 20 Apr 2016, 18:45
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
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 21 Apr 2016, 01:20
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 \(\sqrt{10^2 + 5^2} = 5\sqrt{5}\).

Answer (C)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
User avatar
G
Joined: 09 Jan 2016
Posts: 110
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

New post 30 Apr 2017, 05:37
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}
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51215
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 30 Apr 2017, 06:05
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 467
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l  [#permalink]

Show Tags

New post 23 Aug 2017, 06:24
1
Answer is clearly C as shown in figure.
Attachments

IMG_3955.JPG
IMG_3955.JPG [ 1.67 MiB | Viewed 989 times ]


_________________

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

Intern
Intern
avatar
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]

Show Tags

New post 07 Oct 2018, 01:58
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 ?
GMAT Club Bot
Re: Line L and line K have slopes -2 and 1/2 respectively. If line L and l &nbs [#permalink] 07 Oct 2018, 01:58
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.