Last visit was: 18 Nov 2025, 22:25 It is currently 18 Nov 2025, 22:25
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
dreambeliever
User avatar
Joined: 24 Nov 2010
Last visit: 20 Jun 2013
Posts: 118
Own Kudos:
291
 [51]
Given Kudos: 7
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Duke '15 Ross '15
Schools: Duke '15 Ross '15
Posts: 118
Kudos: 291
 [51]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 30 Nov 2011, 21:37
1
Kudos
Add Kudos
50
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

36% (02:15) correct 64% (02:09) wrong based on 595 sessions

History

Date
Time
Result
Not Attempted Yet
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.
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,104
 [23]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,104
 [23]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 15 Jan 2012, 12:46
10
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
karthiksms
could someone pl explain ? i'm unable to understand answer.
Show more

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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,104
 [9]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,104
 [9]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 15 Jan 2012, 12:48
2
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
karthiksms
could someone pl explain ? i'm unable to understand answer.
Show more

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 20300 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 20215 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 20126 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 20070 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.
General Discussion
User avatar
liftoff
User avatar
Joined: 27 May 2010
Last visit: 27 Sep 2012
Posts: 59
Own Kudos:
16
 [3]
Given Kudos: 8
Status:Essaying
Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE:Accounting (Education)
Schools: Cambridge
GMAT 1: 690 Q47 V37
Posts: 59
Kudos: 16
 [3]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 05 Dec 2011, 08:35
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
User avatar
dreambeliever
User avatar
Joined: 24 Nov 2010
Last visit: 20 Jun 2013
Posts: 118
Own Kudos:
291
Given Kudos: 7
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Duke '15 Ross '15
Schools: Duke '15 Ross '15
Posts: 118
Kudos: 291
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 11 Dec 2011, 13:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
liftoff
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
Show more

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?
User avatar
ronr34
User avatar
Joined: 08 Apr 2012
Last visit: 10 Oct 2014
Posts: 248
Own Kudos:
250
Given Kudos: 58
Posts: 248
Kudos: 250
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 05 Nov 2013, 14:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,311
Own Kudos:
2,863
 [4]
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,311
Kudos: 2,863
 [4]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). Updated on: 18 May 2014, 09:05
Originally posted by jlgdr on 28 Dec 2013, 16:14.
Last edited by jlgdr on 18 May 2014, 09:05, edited 1 time in total.
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
ronr34
Bunuel
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?
Show more

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
avatar
guimooow
avatar
Joined: 13 Dec 2013
Last visit: 18 Mar 2014
Posts: 4
Own Kudos:
6
 [1]
Given Kudos: 26
Posts: 4
Kudos: 6
 [1]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 30 Jan 2014, 09:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amaxing Jlgdr!! thank you buddy. it is so clear now
User avatar
musunna
User avatar
Joined: 14 Sep 2013
Last visit: 12 May 2020
Posts: 88
Own Kudos:
55
Given Kudos: 38
Status:Just redeemed Kudos for GMAT Club Test !!
Location: Bangladesh
Schools: Iowa State '18 Jenkins FT'18 UConn"19 Darden '19
GMAT 1: 530 Q40 V23
GPA: 3.56
WE:Analyst (Commercial Banking)
Schools: Iowa State '18 Jenkins FT'18 UConn"19 Darden '19
GMAT 1: 530 Q40 V23
Posts: 88
Kudos: 55
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 16 May 2016, 18:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel


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

hi Bunuel, I'm not sure how can we come to this equation mentioned above. Would you please explain a bit on this ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,104
 [1]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,104
 [1]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 17 May 2016, 03:52
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
musunna
Bunuel


(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 ?
Show more

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)
avatar
02999
avatar
Joined: 09 Apr 2020
Last visit: 06 May 2023
Posts: 20
Own Kudos:
3
Given Kudos: 516
Posts: 20
Kudos: 3
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 22 Jan 2022, 05:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
karthiksms
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: https://gmatclub.com/forum/math-coordina ... 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.
Show more

why can't we deduce like below -
1/n-1/m >0=> 1/n>1/m=> m>n

Can you please explain.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,104
 [1]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,104
 [1]
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 22 Jan 2022, 08:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
02999
Bunuel
karthiksms
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: https://gmatclub.com/forum/math-coordina ... 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.

why can't we deduce like below -
1/n-1/m >0=> 1/n>1/m=> m>n

Can you please explain.
Show more

You cannot cross-multiply 1/n > 1/m to get m > n because we don't know the signs of m and n. If they have the same sign, then yes, after cross-multiplying we get m > n but if n is positive and m is negative, then after cross-multiplying we get m < n. For example:

If n = 2 and m = 3 --> 1/2 > 1/3 --> 3 > 2;
If n = -3 and m = -2 -->1/(-3) > 1/(-2) --> -2 > -3.

But if n = 2 and m = -2 -->1/2 > 1/(-2) --> -2 < 2.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,583
Own Kudos:
1,079
Posts: 38,583
Kudos: 1,079
Lines m and n lie in the xy-plane and intersect at the point (-2; 4). 30 Nov 2024, 04:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts