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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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.

Graphic approach:

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 (5,1) (2) The y-intercept of line n is greater than y-intercept of line p

The two statements individually are not sufficient.

(1)+(2) Note that a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n:

So in both cases the slope of p is greater than the slope of n. Sufficient.

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.

Re: Lines n and p lie in the xy-plane. Is the slope of line n le [#permalink]

Show Tags

13 Sep 2012, 12:19

monikaleoster 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.

Here we have two lines and two slopes So lets first write the equations for our lovely lines

Y = mnX + Cn Y = mpX + Cp

Now statement one says that it intersects at 5,1. SO lets put it in the equations and subtract them

We get, (mn-mp)5 = Cp-Cn that tells us nothing about the slopes of the lines or their relative values, but if we know the value of Cp-Cn that weather it is positive or negative we will know weathet mn-mp is positive or negative and that which is greater

Statement 2 Y intercept of line n is greater than p so that gives us Cn >Cp

Alone this statement is also not sufficient. it talks abou c not slopes

But if we combine the two, Voila !! we know which slope is greater.

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

29 Dec 2012, 09:18

I don't get it :/

what if slope of line P is positive and the slope of line N negative (but still satisfying all the condition...) Bunuel, on your examples the slopes have the same sign... are we talking about the absolute value of the slope?

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

16 Jul 2013, 19:23

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.

Answer: C.

Hope it helps.

Bunuel,

In here - \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

Why have you chosen different variables for the y?

Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only.

I know I am missing something but I am not clear as to why you have picked different variables for y but not for x.

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.

Hope it helps.

Bunuel,

In here - \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

Why have you chosen different variables for the y?

Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only.

I know I am missing something but I am not clear as to why you have picked different variables for y but not for x.

n and p are subscripts of y's, not variables.

\(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p.

I used subscripts simply to distinguish one equation from another.
_________________

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

17 Jul 2013, 05:02

Bunuel wrote:

keenys wrote:

Bunuel wrote:

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.

Hope it helps.

Bunuel,

In here - \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

Why have you chosen different variables for the y?

Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only.

I know I am missing something but I am not clear as to why you have picked different variables for y but not for x.

n and p are subscripts of y's, not variables.

\(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p.

I used subscripts simply to distinguish one equation from another.

If that is the case then, from the above equations

we get b1=y-m1x and b2=y-m2x

Now from statement 2 we know that b1>b2...

therefore, y-m1x >y-m2x

which gives (m1-m2)x>0

So it can be proved from statement 2 only that m1>m2

In here - \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?

Why have you chosen different variables for the y?

Shouldnt the two equations be y=m1x+b1 and y=m2x+b2? We always form the equation from the basic form of y=mx+c wherein we substitute the values of m and c. And if that is the case, we can get the answer from statement II only.

I know I am missing something but I am not clear as to why you have picked different variables for y but not for x.

n and p are subscripts of y's, not variables.

\(y=m_1x+b_1\) is equation of line n. \(y=m_2x+b_2\) is equation of line p.

I used subscripts simply to distinguish one equation from another.

If that is the case then, from the above equations

we get b1=y-m1x and b2=y-m2x

Now from statement 2 we know that b1>b2...

therefore, y-m1x >y-m2x

which gives (m1-m2)x>0

So it can be proved from statement 2 only that m1>m2

Where am I going wrong?

The y-intercept is the value of \(y\) for \(x=0\). You should substitute x=0 into both equations.

So, the y-intercept of line n is b1 and the y-intercept of line p is b2, from (2) we only have that b1>b2.
_________________

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

28 Dec 2013, 05:57

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.

Graphic approach:

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 (5,1) (2) The y-intercept of line n is greater than y-intercept of line p

The two statements individually are not sufficient.

(1)+(2) Note that a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

Attachment:

1.PNG

If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n:

Attachment:

2.PNG

So in both cases the slope of p is greater than the slope of n. Sufficient.

Answer: C.

So talking about the case with negative slopes here. OK so line 'n' is steeper hence it has a higher absolute value for slope right? Then because it is more negative then it is in fact smaller than the slope of line p.

So here we are saying that the slope is treated just as any number, which means considering its sign

Eg. Slope of an horizontal line will be higher than a negative slope right? Just cause if one does it algebraically one will encounter the comparison and absolute values are not used at all in slope formulae as far as I'm aware

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

02 Sep 2014, 03:54

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.

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.

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

02 Sep 2014, 04:33

Sidhrt 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.

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.

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

20 Sep 2015, 03:14

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.
_________________

Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

06 Jan 2016, 13:43

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.

Hi math experts, I've used the following approach to derive on the correct answer. Would appreciate your input.

(1) It's not possible to calculate the slope with only one point given. Also it's an intersection point which satisfies the equations of both lines. Not Sufficient (2) You cannot determine a slope, with info about y-intercept, one can manipulate randomply the x-line intersection and get diff. results regarding slopes. (1)+(2) We have point (5,1) and info about y intercept. By y-intercept x=0 and we know that line n has a greater y-intercept: Case 1 +ve: Line n (0, 3) and Line p (0, 2) --> Slope n \(= \frac{1-3}{5}=-\frac{2}{5}\), Slope p\(=\frac{1-2}{5}=-\frac{1}{5}\), So Slope p > Slope n Case 2 -ve: Line n (0, -2) and Line p (0, -3) --> Slope n \(= \frac{1-(-2)}{5}=\frac{3}{5}\), Slope p=\(\frac{1-(-3)}{5}=\frac{4}{5}\) Again Slope p > Slope n

Answer C
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

Show Tags

10 Mar 2016, 22:36

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.

Graphic approach:

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 (5,1) (2) The y-intercept of line n is greater than y-intercept of line p

The two statements individually are not sufficient.

(1)+(2) Note that a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

Attachment:

1.PNG

If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n:

Attachment:

2.PNG

So in both cases the slope of p is greater than the slope of n. Sufficient.

Answer: C.

We have tried both slopes negative or both slopes positive, why we didn't tried one slope positive and another negative combination.
_________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

gmatclubot

Re: Lines n and p lie in the xy-plane. Is the slope of line n
[#permalink]
10 Mar 2016, 22:36

Military MBA Acceptance Rate Analysis Transitioning from the military to MBA is a fairly popular path to follow. A little over 4% of MBA applications come from military veterans...

Best Schools for Young MBA Applicants Deciding when to start applying to business school can be a challenge. Salary increases dramatically after an MBA, but schools tend to prefer...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...