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

It is currently 11 Dec 2018, 14:50

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
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Lines m and n lie in the xy-plane and intersect at the point (-2; 4).

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

Hide Tags

Manager
Manager
avatar
Joined: 24 Nov 2010
Posts: 178
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
GMAT ToolKit User
Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 30 Nov 2011, 20:37
1
20
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (01:44) correct 68% (01:43) wrong based on 452 sessions

HideShow timer Statistics

Lines m and n lie in the xy-plane and intersect at the point (-2; 4). Is the slope of line m less than the slope of line n?

(1) The x-intercept of line m is greater than the x-intercept of line n.
(2) The y-intercept of line n is greater than the y-intercept of line m.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 15 Jan 2012, 11:46
5
8
karthiksms wrote:
could someone pl explain ? i'm unable to understand answer.


ALGEBRAIC WAY:
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). Is the slope of line m less than the slope of line n?

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line, \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)), \(-\frac{b}{m}\) is the x-intercept of the line (the value of \(x\) for \(y=0\)). (Check Coordinate Geometry chapter of Math Book for more on this topic: math-coordinate-geometry-87652.html)

We are given two lines: \(y_m=mx+b\) and \(y_n=nx+c\). Now, as they intersect at the point (-2; 4) then: \(4=-2m+b\) and \(4=-2n+c\) (this point is common for both of the lines) --> \(b=4+2m\) and \(c=4+2n\).

Question: is \(m<n\)?

(1) The x-intercept of line m is greater than the x-intercept of line n --> \(-\frac{b}{m}>-\frac{c}{n}\) --> \(-\frac{4+2m}{m}>-\frac{4+2n}{n}\) --> \(\frac{1}{n}-\frac{1}{m}>0\) --> insufficient to answer whether \(m<n\): if \(n=2\) and \(m=-4\) then YES but if \(n=2\) and \(m=4\) then NO. Not sufficient.

(2) The y-intercept of line n is greater than the y-intercept of line m --> \(c>b\) --> \(4+2n>4+2m\) --> \(n>m\). Sufficient.

Answer: B.
_________________

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

General Discussion
Manager
Manager
avatar
Status: Essaying
Joined: 27 May 2010
Posts: 108
Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
GMAT ToolKit User
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 05 Dec 2011, 07:35
1
1
I would go with D.
We are already given one point at the point of intersection.
Statement 1 gives us an extra point therefore we can determine which line is steeper. sufficient
Statement 2 also gives us the same information. sufficient
Manager
Manager
avatar
Joined: 24 Nov 2010
Posts: 178
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
GMAT ToolKit User
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 11 Dec 2011, 12:33
liftoff wrote:
I would go with D.
We are already given one point at the point of intersection.
Statement 1 gives us an extra point therefore we can determine which line is steeper. sufficient
Statement 2 also gives us the same information. sufficient


I was thinking if determining which one is steeper is enough or not.

Per (1) The x-intercept of line m is greater than the x-intercept of line n.

so line m can have a slope of lets say -2. If line n also has a -ve slope then it will need to be 'flatter' than line m for its x intercept to be greater than that of line m. So its slope will need to be > -2 (for -ve slopes flatter line are closer to 0 that slopes of steeper lines). so in this case slope of line n can be something like -1. So slope of n > slope of m (-1>-2).
however, if slope of m is lets say 2, slope of n can be -ve like -2 with a greater x intercept. This satisfies the condition 1, but slope of m> slope of n in this case (2>-2).
Hence, (1) is insufficient.

Similarly we can prove for the y intercept in case of 2nd statement.

The 2 statements taken together, they should still be insufficient.

OA is D. But i'm having trouble understanding it.

Can someone please explain if I'm wrong?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 15 Jan 2012, 11:48
2
4
karthiksms wrote:
could someone pl explain ? i'm unable to understand answer.


GRAPHIC APPROACH:
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). Is the slope of line m less than the slope of line n?

(1) The x-intercept of line m is greater than the x-intercept of line n. Draw lines:
Case A:
Attachment:
graph.png
graph.png [ 8.32 KiB | Viewed 8623 times ]
Red lines represent possible position of line m and blue line possible position of line n. (You can see that x-intercept of red lines>x-intercept of blue line, so the condition in the statement is satisfied).
In the first case, both slopes are positive and red line (m) is steeper than blue line (n) which means that slope of line m>slope of line n (a steeper incline indicates a higher slope absolute value).

Case B:
Attachment:
graph 2.png
graph 2.png [ 8.56 KiB | Viewed 8616 times ]
In this case, the slope of n is positive ans the slope of m is negative, hence slope of line n>slope of line m.

Two different answers. Not sufficient.

(2) The y-intercept of line n is greater than the y-intercept of line m. Draw lines:
Case A:
Attachment:
graph 3.png
graph 3.png [ 8.28 KiB | Viewed 8613 times ]
In the first case, both slopes are positive and blue line (n) is steeper than red line (m) which means that slope of line n>slope of line m (a steeper incline indicates a higher slope absolute value).Sufficient.

Case B:
Attachment:
graph 4.png
graph 4.png [ 7.92 KiB | Viewed 8602 times ]
In this case, both slopes are negative and red line (m) is steeper than blue line (m), so the slope of m is more negative than slope of n (|m|>|n| --> -m>-n --> n>m), which again means that slope of line n>slope of line m.Sufficient.

Answer: B.

Similar question: lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-97007.html?hilit=more%20negative%20slope%20steeper#p747640

Hope it's clear.
_________________

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
avatar
Joined: 07 Apr 2012
Posts: 369
Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 05 Nov 2013, 13:46
I have seen a lot of examples of this question, and every time it comes down to the Y intercept.
Can we use this as a shortcut? can we make a generalization here?
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1728
Concentration: Finance
GMAT ToolKit User
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post Updated on: 18 May 2014, 08:05
2
1
ronr34 wrote:
Bunuel wrote:
Bumping for review and further discussion.

I have seen a lot of examples of this question, and every time it comes down to the Y intercept.
Can we use this as a shortcut? can we make a generalization here?


Yes we can use something else other than the graph method, which I find a little bit difficult to follow on many cases.

Let's see we need to know if m>n or if m-n>0, 'm and 'n' being the slopes of the respective lines

We know that they intersect at point (-2,4)

Then we have Line m= y = mx + b ---> 4 = -2m +b
Line n = y = nx+c---> 4=-2n+c

Both equal, -2n+c= -2m+b
2m-2n = b-c
m-n = (b-c)/2

Now going back to the question.

Is b-c/2 > 0?

is b-c>0, is b-c?

Statement 1

We are given that -b/m>-c/n
-bn>-cm

We can't tell whether b>c
Insuff

Statement 2

This is exactly what we were looking for
b>c

Sufficient

B stands

Hope its clear
Cheers!
J :)

YES YOU CAN

Originally posted by jlgdr on 28 Dec 2013, 15:14.
Last edited by jlgdr on 18 May 2014, 08:05, edited 1 time in total.
Intern
Intern
avatar
Joined: 13 Dec 2013
Posts: 5
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 30 Jan 2014, 08:55
1
amaxing Jlgdr!! thank you buddy. it is so clear now
Manager
Manager
User avatar
S
Status: Just redeemed Kudos for GMAT Club Test !!
Joined: 14 Sep 2013
Posts: 94
Location: Bangladesh
GMAT 1: 530 Q40 V23
GPA: 3.56
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 16 May 2016, 17:59
Bunuel wrote:

(1) The x-intercept of line m is greater than the x-intercept of line n --> \(-\frac{b}{m}>-\frac{c}{n}\)


hi Bunuel, I'm not sure how can we come to this equation mentioned above. Would you please explain a bit on this ?
_________________

______________
KUDOS please, if you like the post or if it helps :-)
"Giving kudos" is a decent way to say "Thanks"

Master with structure - Numerical comparison [source: economist.com] https://gmatclub.com/forum/master-with-structure-numerical-comparison-233657.html#p1801987

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: Lines m and n lie in the xy-plane and intersect at the point  [#permalink]

Show Tags

New post 17 May 2016, 02:52
musunna wrote:
Bunuel wrote:

(1) The x-intercept of line m is greater than the x-intercept of line n --> \(-\frac{b}{m}>-\frac{c}{n}\)


hi Bunuel, I'm not sure how can we come to this equation mentioned above. Would you please explain a bit on this ?


I think this is explained here: slopes-of-m-and-n-124025.html#p1029568

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line, \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)),\(-\frac{b}{m}\) is the x-intercept of the line (the value of \(x\) for \(y=0\)). (Check Coordinate Geometry chapter of Math Book for more on this topic: math-coordinate-geometry-87652.html)
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9117
Premium Member
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4).  [#permalink]

Show Tags

New post 02 Oct 2018, 09:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Lines m and n lie in the xy-plane and intersect at the point (-2; 4). &nbs [#permalink] 02 Oct 2018, 09:32
Display posts from previous: Sort by

Lines m and n lie in the xy-plane and intersect at the point (-2; 4).

  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®.