Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 Oct 2015, 00:06

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Lines m and n lie in the xy-plane and intersect at the point

Author Message
TAGS:
Manager
Joined: 24 Nov 2010
Posts: 209
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 51 [0], given: 7

Lines m and n lie in the xy-plane and intersect at the point [#permalink]  30 Nov 2011, 20:37
3
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

29% (02:53) correct 71% (01:32) wrong based on 227 sessions
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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 29679
Followers: 4889

Kudos [?]: 53114 [3] , given: 8043

Re: slopes of m and n [#permalink]  15 Jan 2012, 11:46
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 29679
Followers: 4889

Kudos [?]: 53114 [2] , given: 8043

Re: slopes of m and n [#permalink]  15 Jan 2012, 11:48
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 [ 8.32 KiB | Viewed 4091 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 [ 8.56 KiB | Viewed 4090 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.

(2) The y-intercept of line n is greater than the y-intercept of line m. Draw lines:
Case A:
Attachment:

graph 3.png [ 8.28 KiB | Viewed 4091 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 [ 7.92 KiB | Viewed 4084 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.

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.
_________________
SVP
Joined: 06 Sep 2013
Posts: 2045
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 33

Kudos [?]: 366 [2] , given: 355

Re: Lines m and n lie in the xy-plane and intersect at the point [#permalink]  28 Dec 2013, 15:14
2
KUDOS
1
This post was
BOOKMARKED
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

Last edited by jlgdr on 18 May 2014, 08:05, edited 1 time in total.
Intern
Joined: 13 Dec 2013
Posts: 6
Followers: 0

Kudos [?]: 3 [1] , given: 26

Re: Lines m and n lie in the xy-plane and intersect at the point [#permalink]  30 Jan 2014, 08:55
1
KUDOS
amaxing Jlgdr!! thank you buddy. it is so clear now
Manager
Status: Essaying
Joined: 27 May 2010
Posts: 154
Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
Followers: 1

Kudos [?]: 9 [0], given: 8

Re: slopes of m and n [#permalink]  05 Dec 2011, 07:35
1
This post was
BOOKMARKED
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
Joined: 24 Nov 2010
Posts: 209
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 51 [0], given: 7

Re: slopes of m and n [#permalink]  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
Joined: 02 Sep 2009
Posts: 29679
Followers: 4889

Kudos [?]: 53114 [0], given: 8043

Re: Lines m and n lie in the xy-plane and intersect at the point [#permalink]  22 May 2013, 02:40
Expert's post
Bumping for review and further discussion.
_________________
Senior Manager
Joined: 07 Apr 2012
Posts: 464
Followers: 1

Kudos [?]: 27 [0], given: 58

Re: Lines m and n lie in the xy-plane and intersect at the point [#permalink]  05 Nov 2013, 13:46
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?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6697
Followers: 365

Kudos [?]: 82 [0], given: 0

Re: Lines m and n lie in the xy-plane and intersect at the point [#permalink]  20 May 2015, 02:43
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.
_________________
Re: Lines m and n lie in the xy-plane and intersect at the point   [#permalink] 20 May 2015, 02:43
Similar topics Replies Last post
Similar
Topics:
3 The lines m, l, and n intersect at point Q. What are the mea 5 15 Jun 2013, 04:43
39 Lines n and p lie in the xy-plane. Is the slope of line n 17 23 Feb 2012, 07:07
11 In the xy-plane, does the point (-3; 3) lie on line k? 4 14 Feb 2012, 07:55
7 In the xy-plane, line l and line k intersect at the point 6 26 Sep 2010, 10:49
In the xy-plane, line l and line k intersect at the point 1 05 Jan 2010, 07:00
Display posts from previous: Sort by