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

It is currently 24 May 2019, 03:37

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

If k and ℓ are lines in the xy-plane, is the slope of k less than the

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55272
If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 02 Aug 2018, 23:58
2
19
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (01:25) correct 33% (01:26) wrong based on 499 sessions

HideShow timer Statistics

If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?


(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.


NEW question from GMAT® Quantitative Review 2019


(DS13097)

_________________
Most Helpful Expert Reply
MBA Section Director
User avatar
V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2521
GPA: 4
WE: Engineering (Computer Software)
GMAT ToolKit User Premium Member Reviews Badge
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 03 Aug 2018, 02:27
5
3
To find if the slope of k less than the slope of ℓ

Statement 1

The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

Case 1

K can have a +ve slope when k rises upward while running from left to right and ℓ can have a -ve slope when ℓ slides downward while running from left to right

=> slope of line k > slope of line ℓ

Case 2

K can have a -ve slope when k slides downwards while running from left to right and ℓ can have a +ve slope when ℓ rises upward while running from left to right

=> slope of line k < slope of line ℓ

Statement 1 is not sufficient

Statement 2

Lines k and ℓ intersect on the positive y-axis. Both the above mentioned cases are still possible

Statement 2 is not sufficient

Combining statements 1 and 2

Since x-intercept of line k is positive and y-intercept of line k is positive => K has negative slope

Since x-intercept of line ℓ is negative and y-intercept of line ℓ is positive => ℓ has positive slope

=> slope of line ℓ > slope of line k

Statements 1 and 2 together are sufficient

Hence option C
_________________
General Discussion
Intern
Intern
avatar
Joined: 17 Aug 2015
Posts: 6
Location: India
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 05 Aug 2018, 12:23
Equation: y=mx+c

Case 1 for line k: x intercept is -c/m>0
Case 1 for line l: x intercept is -c/m<0

Statement 1 is not Sufficient as in both the cases, either c could be -ve or m could be -ve

Case 2: Y intercept is positive => c is positive in the equation for both lines

Statement 2 is not Sufficient as in both the cases, slope information is not there

Combining

Case 1 for line k: x intercept is -c/m>0 , given c >0 , m is -ve
Case 1 for line l: x intercept is -c/m<0, given c>0, m is +ve

=> slope l>slope k or slope k<slope l - Sufficient

C

Hope this helps! :-)
Senior Manager
Senior Manager
User avatar
G
Joined: 29 Dec 2017
Posts: 384
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 06 Sep 2018, 08:12
I cannot emphasize more: 99.99% of xy-plane questions (DS/PS) can be solved by drawing. Don't mess with formulas here.
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 514
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 18 Oct 2018, 09:14
1
1
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?


(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.


NEW question from GMAT® Quantitative Review 2019


(DS13097)


Best way to solve it is to draw

Refer to the drawings to have an idea of how I solved it.

answer choice C
Attachments

File comment: This is how it can be solved if combined
Combined.png
Combined.png [ 39.73 KiB | Viewed 3043 times ]

File comment: This is one example of how many different ways we can get for statement 2
Statement 2.png
Statement 2.png [ 45.32 KiB | Viewed 3045 times ]

File comment: This is one example of how many different ways we can get for statement 1
Statement 1.png
Statement 1.png [ 37.38 KiB | Viewed 3041 times ]

Manager
Manager
avatar
B
Joined: 29 Oct 2015
Posts: 138
If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 13 Apr 2019, 15:11
@Bunuel

@VeritasKarishma

@Chetan2u

If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?


(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

Statement 1 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.

(2) Lines k and ℓ intersect on the positive y-axis.

Statement 2 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.


Combining it's sufficient as it leads to only one possibility i.e SLope of L is greater than slope of K.

Answer is option C.


I have attached three images in support of my explanation.

Please find them attached herewith.

Please Please give me kudos if you found my explanation helpful.


NEW question from GMAT® Quantitative Review 2019


(DS13097)[/quote]
Attachments

20190414_032153_Combining.jpg
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 809 times ]

20190414_031608_Statement2.jpg
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 808 times ]

20190414_030550_Statement1.jpg
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 810 times ]

20190414_030550_Statement1.jpg
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 943 times ]

20190414_032153_Combining.jpg
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 943 times ]

20190414_031608_Statement2.jpg
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 945 times ]

Manager
Manager
avatar
B
Joined: 29 Oct 2015
Posts: 138
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 17 Apr 2019, 21:02
VeritasKarishma

Bunuel

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9237
Location: Pune, India
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 17 Apr 2019, 23:29
1
1
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?


(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.


NEW question from GMAT® Quantitative Review 2019


(DS13097)


Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept)

Is slopek < slopel ?
Is - yk / xk < - yl / xl ?
Is yk / xk > yl / xl ?

(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

xk > 0
xl < 0

Since we don't know anything about yk and yl, this is not sufficient.


(2) Lines k and ℓ intersect on the positive y-axis.

This means both yk and yl are positive. But we don't know anything about xk and xl.

Using both, yk/xk is positive because both yk and xk are positive.
yl/xl is negative because yl is positive but xl is negative.
Then, yk / xk is certainly greater than yl / xl.

Sufficient. 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
avatar
B
Joined: 29 Oct 2015
Posts: 138
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 18 Apr 2019, 03:00
Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 17 May 2018
Posts: 137
Location: India
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 18 Apr 2019, 03:10
Statement 1 gives us part of the information
Stating that the intercepts are positive and negative for the 2 lines.
Statement 2 gives us the part of the information that y intercept is +ve for both lines.
Both statements together gives us the solution.
IMO C

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9237
Location: Pune, India
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

Show Tags

New post 18 Apr 2019, 19:41
sayan640 wrote:
Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?

Posted from my mobile device


Sayan60,

Certainly there is nothing wrong with graphing out the question and I am a big proponent of making diagrams etc. Just that with multiple lines and slopes and various constraints given in the statements, I find it a bit confusing and worry about missing a case or two. So I have found that the slope and intercept method I discussed above is far more efficient in these cases.
_________________
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 >
GMAT Club Bot
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the   [#permalink] 18 Apr 2019, 19:41
Display posts from previous: Sort by

If k and ℓ are lines in the xy-plane, is the slope of k less than the

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


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®.