GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 Apr 2018, 10:59

### 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 n and p lie in the xy-plane. Is the slope of line n

Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8025
Location: Pune, India
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

23 Oct 2016, 23:38
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

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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

SVP
Joined: 08 Jul 2010
Posts: 2068
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

13 Nov 2016, 07:02
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.

Check the cases as per color coding
Attachments

File comment: www.GMATinsight.com

15.jpg [ 112.57 KiB | Viewed 696 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 08 May 2016
Posts: 30
Location: United States
WE: Project Management (Aerospace and Defense)
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

30 Nov 2016, 14:11
Here is a great resource to understand slope. You can plug in values and see how things change:
https://www.desmos.com/calculator/nuokqfhfxi

Hope this helps
_________________

Manager
Joined: 19 Aug 2016
Posts: 151
Location: India
GMAT 1: 640 Q47 V31
GPA: 3.82
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

22 Apr 2017, 14:23
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.

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

Hope it helps.

Hi Bunuel,

Can you share some similar questions to practice on this topic? Also, what would be the level of such a question? <650?
_________________

Consider giving me Kudos if you find my posts useful, challenging and helpful!

Math Expert
Joined: 02 Sep 2009
Posts: 44655
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

23 Apr 2017, 03:28
ashikaverma13 wrote:
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.

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

Hope it helps.

Hi Bunuel,

Can you share some similar questions to practice on this topic? Also, what would be the level of such a question? <650?

The difficulty level of a question is given in the tags. It's 600-700 level question.

All DS Coordinate Geometry Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=41
All PS Coordinate Geometry Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=62

Hope it helps.
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2298
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

07 Dec 2017, 10:50
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.

We need to determine whether the slope of line n is less than the slope of line p.

Statement One Alone:

Lines n and p intersect at the point (5,1).

If the two lines intersect at a point, they are not parallel and hence their slopes are not equal (unless they are identical lines). So the slope of one line must be greater than the slope of the other line. However, we can’t determine which line has the greater slope. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

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

Knowing that the y-intercept of one line is greater than the y-intercept of the other does not allow us to determine which line has the greater slope.

For example, line n could have a y-intercept 2 and slope 3, and line p could have a y-intercept 1 and slope 2. In this case, line p has the lesser slope. However, it’s also possible that line n could have a y-intercept 2 and slope 2, and line p could have a y-intercept 1 and slope 3. In which case, line n has the lesser slope. Statement two alone is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Knowing the point where the two lines intersect and the relationship of the y-intercept of each line allows us to determine which line has the lesser slope.

Even though we don’t know the actual y-intercept of each line, we know that the y-intercept of line n is greater than that of line p. So we can let the y-intercept of line n be b, and that of line p be c where b > c.

Thus, line n passes through (0, b), and line p passes through (0, c). Both lines also pass through (5, 1). Let’s calculate their slopes:

Slope of line n = (1 – b)/(5 – 0) = (1 – b)/5

Slope of line p = (1 – c)/(5 – 0) = (1 – c)/5

Now let’s determine whether (1 – b)/5 < (1 – c)/5.

Is (1 – b)/5 < (1 – c)/5 ?

Is 1 – b < 1 – c ?

Is –b < –c ?

Is b > c ?

Since, from the information in statement two, we know that b is greater than c, we have answered the question: the slope of line n is indeed less than that of line p.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 14 Sep 2016
Posts: 16
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

13 Dec 2017, 21:35
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.
Math Expert
Joined: 02 Sep 2009
Posts: 44655
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

13 Dec 2017, 21:38
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.
_________________
Intern
Joined: 20 Feb 2018
Posts: 2
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

12 Mar 2018, 08:35
What if the slope of n is negative and the slope of p is positive?
Math Expert
Joined: 02 Sep 2009
Posts: 44655
Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

12 Mar 2018, 08:40
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".
_________________
Intern
Joined: 20 Feb 2018
Posts: 2
Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

### Show Tags

12 Mar 2018, 10:10
Bunuel wrote:
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".

Got it and thanks! My diagram was off. I didn't see that the slope of n couldn't be made positive without violating that condition.
Lines n and p lie in the xy-plane. Is the slope of line n   [#permalink] 12 Mar 2018, 10:10

Go to page   Previous    1   2   [ 31 posts ]

Display posts from previous: Sort by