NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 11:21 It is currently 13 May 2024, 11:21
Decision Tracker
My Rewards
New posts
New comers' posts

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

Lines n and p lie in the xy-plane. Is the slope of line n less than th

SORT BY:
Date
Kudos
   1   2 
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65265 [0]
Given Kudos: 431
Location: Pune, India
Send PM
Forum Quiz Mode
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   23 Oct 2016, 23:38
Expert Reply
rohit8865 wrote:
Bunuel wrote:
nglekel wrote:
Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?




If line p has a negative y-intercept then its slope is positive and it will still be more than the slope of n, with positive y-intercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive y-intercept and you'll easily see the answer.


Hope it helps.


Experts

Please reply for my doubt.....
for below attached fig ...getting 2 diff.. answers.....


Responding to a pm:

I am not sure I understand why you say you are getting two different answers. In both diagrams, the slope of n is less than the slope of p. We are comparing actual values of the slopes, not just the absolute values.
So say slope of n is -2 in both cases. Slope of p in the first diagram will be -1/2 and slope of p in the second diagram would be about 1.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93242
Own Kudos [?]: 623469 [0]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   13 Dec 2017, 21:38
Expert Reply
dramamur wrote:
Am I right in my understanding that since the question asks for whether the slope of line n is greater than the slope of p, we need to consider only actual values and not absolute values.

If the question had asked for whether line n is steeper than line p, then we would have had to consider absolute values and in this second case, the answer will actually have been E?

Bunuel or Karishma or other experts please clarify.


Yes, the question asks whether \(m_1<m_2\) is true (not whether \(|m_1|<|m_2|\) is true). Every solution on the previous two pages answers exactly this question.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93242
Own Kudos [?]: 623469 [0]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   12 Mar 2018, 08:40
Expert Reply
thorohhh wrote:
What if the slope of n is negative and the slope of p is positive?


This would contradict the second statement: "The y-intercept of line n is greater than the y-intercept of line p".
avatar
B
aaronhew
Intern
Intern
Joined: 06 Jun 2017
Posts: 7
Own Kudos [?]: 1 [0]
Given Kudos: 60
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   16 May 2018, 05:51
If you try to gauge the difficulty of this question, would it be a 400-level question, 500-level, 600-level, etc?

Coordinate plane questions tend to be most difficult for me right now. I'm working on my ability to solve these types. So, it would be helpful to be able to gauge the degree of difficulty for problems that trouble me.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5975
Own Kudos [?]: 13469 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge Forum Quiz Mode
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   16 May 2018, 06:11
Expert Reply
aaronhew wrote:
If you try to gauge the difficulty of this question, would it be a 400-level question, 500-level, 600-level, etc?

Coordinate plane questions tend to be most difficult for me right now. I'm working on my ability to solve these types. So, it would be helpful to be able to gauge the degree of difficulty for problems that trouble me.



This question is fairly difficult.

Given me a chance to rate this question, I would rate it as 700 difficulty level question. Although every question on GMAT CLUB has difficulty level tagged in it.
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1064
Own Kudos [?]: 2125 [0]
Given Kudos: 77
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   03 Jun 2019, 00:30
Statement 1 and 2 are not sufficient by their own.

Attachment:
Soln.jpeg
Soln.jpeg [ 143.12 KiB | Viewed 4606 times ]


Option C is the correct Answer
avatar
B
annezhu
Intern
Intern
Joined: 03 Aug 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 27
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   13 Oct 2019, 21:28
3 conditions:
both slopes are positive: Kp>Kn>0
both slopes are negative: Kn<Kp<0
slope of line n is negative and slope of line p is positive: Kn<0<Kp

the slope of n is less than the slope of p (Kn<Kp) in all the three conditions.
Thus, choose C
User avatar
P
BoundMan
Current Student
Joined: 20 Jun 2018
Posts: 226
Own Kudos [?]: 255 [0]
Given Kudos: 121
Send PM
Reviews Badge
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   27 Nov 2019, 21:15
Hi chetan2u

I see that there are two groups in the above discussion.
I am part of the group that still believes E is the answer.

The y-intercept of line n is greater than the y-intercept of line p.

For example, y-intercept of line n is 6
y-intercept of line P is -19

But if line n can be a downward sloping line while line P could be upward sloping.
In that case, Line P will not have have less slope than Line N?
What am I missing here?
User avatar
P
BoundMan
Current Student
Joined: 20 Jun 2018
Posts: 226
Own Kudos [?]: 255 [0]
Given Kudos: 121
Send PM
Reviews Badge
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   27 Nov 2019, 21:22
chetan2u,

So the question becomes do the lines need to be in the same direction? How do we know that?
User avatar
P
BoundMan
Current Student
Joined: 20 Jun 2018
Posts: 226
Own Kudos [?]: 255 [0]
Given Kudos: 121
Send PM
Reviews Badge
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   29 Nov 2019, 17:51
Hello @VeritasKarishma- do the lines need to be in the same direction? How do we know that?

I think I am missing something here.
User avatar
P
LoneSurvivor
Senior Manager
Senior Manager
Joined: 23 Nov 2016
Posts: 312
Own Kudos [?]: 697 [0]
Given Kudos: 156
GMAT 1: 690 Q50 V33
Send PM
GMAT ToolKit User Reviews Badge
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   25 Dec 2019, 23:37
I agree with you, I have similar doubt and had marked E. Experts please clarify ,by algebra it is coming C as @Bunnel did it right but by Graph approach answer is coming E.

akash7gupta11 wrote:
Hello @VeritasKarishma- do the lines need to be in the same direction? How do we know that?

I think I am missing something here.
User avatar
P
jabhatta2
VP
VP
Joined: 15 Dec 2016
Posts: 1367
Own Kudos [?]: 209 [0]
Given Kudos: 189
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   29 Apr 2020, 15:07
BoundMan wrote:
Hi chetan2u

I see that there are two groups in the above discussion.
I am part of the group that still believes E is the answer.

The y-intercept of line n is greater than the y-intercept of line p.

For example, y-intercept of line n is 6
y-intercept of line P is -19

But if line n can be a downward sloping line while line P could be upward sloping.
In that case, Line P will not have have less slope than Line N?
What am I missing here?


Your test case in red is accurate. Slope of P will be > Slope of N in this test case mentioned in red

In every other test case, taking into account both S1 and S2 -- it always turns out the slope of P > Slope of N

Given the answer is consistently, slope of P > Slope of N in every test case .. the answer to the question [Is the slope of line n less than the slope of line p ?] is consistently in every test case "No"

Hence, s1 and s2 together are sufficient to answer the question
User avatar
G
CEdward
VP
VP
Joined: 11 Aug 2020
Posts: 1259
Own Kudos [?]: 203 [0]
Given Kudos: 332
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   28 Apr 2021, 15:10
GMATinsight wrote:
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.



Answer: Option C

Check the cases as per color coding


For the combined case, why can't we easily switch the n and p pink lines? To me you can get 2 different answers and it should be E.
avatar
B
BharatTj
Intern
Intern
Joined: 21 Aug 2020
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 183
Location: India
Concentration: International Business, Operations
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   27 May 2021, 01:45
VeritasKarishma Please check the final answer and tell me where went wrong. As other posts are saying that slope of n < slope of p

statement 1:
passing via (5,1)

line n 1=5m1+n
line p 1=5m2+p

Statement 2:
n>p

1+2


m1= 1-n/5
m2 = 1-p/5

both 5 gets canceled

1- n and 1-p
n>p

let n=3 p=2
1-3 and 1-2
-2 and -1
m1=2 and m2=1
m1>m2
slope of n>slope of P
User avatar
S
woohoo921
Director
Director
Joined: 04 Jun 2020
Posts: 551
Own Kudos [?]: 69 [0]
Given Kudos: 626
Send PM
Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   18 Nov 2022, 11:06
Bunuel wrote:
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.


Algebraic approach:

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

(1) Lines n and p intersect at the point (5,1) --> \(1=5m_1+b_1=5m_2+b_2\) --> \(5(m_1-m_2)=b_2-b_1\). Not sufficient.

(2) The y-intercept of line \(n\) is greater than the y-intercept of line \(p\) --> y-intercept is value of \(y\) for \(x=0\), so it's the value of \(b\) --> \(b_1>b_2\) or \(b_2-b_1<0\). Not sufficient.

(1)+(2) \(5(m_1-m_2)=b_2-b_1\), as from (2) \(b_2-b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1-m_2)<0\) --> \(m_1-m_2<0\) --> \(m_1<m_2\). Sufficient.

Answer: C.

For more on this topic check Coordinate Geometry Chapter of Math Book: https://gmatclub.com/forum/math-coordina ... 87652.html

Hope it helps.

Bunuel
I ended up using smart numbers

Let's say for line n that b =6 and for line p that b=4

Line n --> y=mx+6

Line p --> y=mx+4

I then plugged in the point (5,1) to find the slope of each equation

Line n's equation ends up being --> y=-x+6
Line p's equation ends up being --> y=-3/5x+4

So, the slope of line n is less than the slope of line p.

Is this an okay approach, or did I just stumble upon the answer?
User avatar
B
pdfff
Intern
Intern
Joined: 10 Mar 2023
Posts: 9
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   03 Jun 2023, 06:14
    avigutman sir can you help me with this problem
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
User avatar
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1301
Own Kudos [?]: 2236 [0]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink] New post   03 Jun 2023, 16:29
Expert Reply
pdfff wrote:
    avigutman sir can you help me with this problem

Happy to, pdfff. Why don't you first walk me through your thinking, so I can better assist you.
GMAT Club Bot
gmatclubot
Re: Lines n and p lie in the xy-plane. Is the slope of line n less than th [#permalink]
03 Jun 2023, 16:29
   1   2 
Moderator:
Bunuel
Math Expert
93242 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions