Last visit was: 17 Jun 2024, 01:23 It is currently 17 Jun 2024, 01:23
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In the xy-plane, lines k and l intersect at the point (1,1). Is the y-

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 09 Jan 2016
Status:Persevere
Posts: 107
Own Kudos [?]: 3675 [420]
Given Kudos: 94
Location: Hong Kong
GMAT 1: 750 Q50 V41
GPA: 3.52
Intern
Joined: 28 Dec 2010
Posts: 19
Own Kudos [?]: 232 [103]
Given Kudos: 337
Retired Moderator
Joined: 05 Jul 2006
Posts: 848
Own Kudos [?]: 1570 [34]
Given Kudos: 49
Manager
Joined: 07 Aug 2018
Posts: 87
Own Kudos [?]: 265 [26]
Given Kudos: 247
Location: United States (MA)
GMAT 1: 560 Q39 V28
GMAT 2: 670 Q48 V34
In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
16
Kudos
10
Bookmarks
I had a really hard time following and understanding the above discussion... Therefore I tried to use a more graphical approach and see how S(1) is sufficient!

We should consider 3 cases for S(1): Booth slopes are negative, booth slopes are positive, and slope $$K$$ is negative and slope $$L$$ is positive.

Case 1. Negative
$$Line K:$$$$y=-2x+3$$
$$Line L:$$$$y=-1x+2$$
Attachment:

1.png [ 29.34 KiB | Viewed 32310 times ]

Case 2. Positive
$$Line K:$$$$y=2x-1$$
$$Line L:$$$$y=3x-2$$
Attachment:

2.png [ 27.98 KiB | Viewed 32173 times ]

Case 3. $$K$$ negative and $$L$$ positive
$$Line K:$$$$y=-2x+3$$
$$Line L:$$$$y=3x-2$$
Attachment:

3.png [ 28.66 KiB | Viewed 32031 times ]

We can see in every case $$K$$ has a higher y intercept than $$L$$.

Therefore S(1) is sufficient and A is the answer.
General Discussion
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11443
Own Kudos [?]: 33518 [57]
Given Kudos: 317
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
19
Kudos
37
Bookmarks
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A
Intern
Joined: 28 Dec 2010
Posts: 19
Own Kudos [?]: 232 [0]
Given Kudos: 337
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Thanks, chetan2u great response. I am trying to understand the relationship of the slope and y intercept. I think irrespective of the line is increasing or decreasing the slope defines lines steepness w.r.t the y -axis. Thus, as we increase the slope our y -intercept should increase. [considering both the line don't have a common intersecting point on the y-axis]. Please let me know if my understanding is correct?
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11443
Own Kudos [?]: 33518 [3]
Given Kudos: 317
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
2
Bookmarks
gary391 wrote:
chetan2u wrote:
nalinnair wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive....
so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value...
At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of $$k$$ is less than the slope of $$l$$.
As seen above y intercept of line l will be more than line k...
Suff

(2) The slope of $$l$$ is positive.
we require to know slope of line k also
Insuff

A

Thanks, chetan2u great response. I am trying to understand the relationship of the slope and y intercept. I think irrespective of the line is increasing or decreasing the slope defines lines steepness w.r.t the y -axis. Thus, as we increase the slope our y -intercept should increase. [considering both the line don't have a common intersecting point on the y-axis]. Please let me know if my understanding is correct?

Hi...

If you just take the absolute value, yes with change in x as constant, change in y will be as per your understanding..

The slope depends on change in value of both x and y.
Numerator has change in y, so more the change more the slope
Denominator has change in x, so less the change more the slope

But the slope can be of two types..
From left bottom to right top...... Both change in x and y will be POSITIVE, so slope is POSITIVE
From left top to bottom right......Change in y is NEGATIVE and change in x will be POSITIVE, so slope is -/+= NEGATIVE even if the absolute value or steepness is MORE
Manager
Joined: 07 Jun 2017
Posts: 81
Own Kudos [?]: 20 [0]
Given Kudos: 454
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me
Attachments

line.PNG [ 5.52 KiB | Viewed 33681 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 93701
Own Kudos [?]: 632385 [4]
Given Kudos: 82322
In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
4
Kudos
pclawong wrote:
In the $$xy$$-plane, lines $$k$$ and $$l$$ intersect at the point $$(1,1)$$. Is the $$y$$-intercept of $$k$$ greater than the $$y$$-intercept of $$l$$?

(1) The slope of $$k$$ is less than the slope of $$l$$.
(2) The slope of $$l$$ is positive.

let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. They will look like as below:

Attachment:

Untitled.png [ 10.79 KiB | Viewed 35942 times ]
Manager
Joined: 07 Jun 2017
Posts: 81
Own Kudos [?]: 20 [1]
Given Kudos: 454
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
1
Bookmarks
Bunuel wrote:
pclawong wrote:
let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below:

Attachment:
Untitled.png

Oh yea, I mean the red line is K
and the blue line is L
so then, even the slope L is larger than slope K,
y intercept of K is still larger than L
am I correct?
that means, statement 1 is not suff.
we also need to know if it is positive slope or negative
Math Expert
Joined: 02 Sep 2009
Posts: 93701
Own Kudos [?]: 632385 [10]
Given Kudos: 82322
Re: In the xy-plane, lines k and l intersect at the point (1,1) [#permalink]
7
Kudos
3
Bookmarks
pclawong wrote:
Bunuel wrote:
pclawong wrote:
let say Ml= -4
Mk= -6
then the slope of k is less than slope of L
y intercept K is greater than L

so I think we need both statement to confirm.
isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below:

Attachment:
Untitled.png

Oh yea, I mean the red line is K
and the blue line is L
so then, even the slope L is larger than slope K,
y intercept of K is still larger than L
am I correct?
that means, statement 1 is not suff.
we also need to know if it is positive slope or negative

(1) says that the slope of $$k$$ is less than the slope of $$l$$. So, in my image BLUE line is K (slope -6) and the RED line is L (slope -4).

As you can see the y-intercept of K is greater than the y-intercept of L. For (1) the y-intercept of K will always be greater than the y-intercept of L.
Intern
Joined: 01 Dec 2017
Posts: 10
Own Kudos [?]: 3 [0]
Given Kudos: 15
Location: Italy
Schools: IMD Jan'18
GMAT 1: 680 Q46 V38
GPA: 4
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?
Math Expert
Joined: 02 Sep 2009
Posts: 93701
Own Kudos [?]: 632385 [0]
Given Kudos: 82322
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
teone83 wrote:
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?

A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0.

Statement (1) says that "The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical.
Math Expert
Joined: 02 Sep 2009
Posts: 93701
Own Kudos [?]: 632385 [0]
Given Kudos: 82322
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
Bunuel wrote:
teone83 wrote:
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or (-) infinite...? In this case how can you say that 1) is suff, since you don't have any value of y-intercept for line k ?

A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0.

Statement (1) says that "The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical.

24. Coordinate Geometry

For other subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [8]
Given Kudos: 799
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
6
Kudos
2
Bookmarks
Top Contributor
nalinnair wrote:
In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Given: In the xy-plane, lines k and l intersect at the point (1,1).

Target question: Is the y-intercept of k greater than the y-intercept of l?

Statement 1: The slope of k is less than the slope of l.
Let's examine 2 cases, and then make a generalization.

CASE A) the slope of line k is POSITIVE
For example, let's say line k has slope 1.

If line l has a greater slope (like a slope of 2), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope of 3, 4, 5, 6 etc , it will always be the case that the y-intercept of k IS greater than the y-intercept of l

CASE B) the slope of line k is NEGATIVE
For example, let's say line k has slope -1.5

If line l has a greater slope (like a slope of -0.6), we can see that the y-intercept of k IS greater than the y-intercept of l
We can further see that if line l has a slope that's greater than line k, it will always be the case that the y-intercept of k IS greater than the y-intercept of l

In both of the above cases, the answer to the target question will be the y-intercept of k IS greater than the y-intercept of l 00
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The slope of l is positive.
Statement 2 is NOT SUFFICIENT

Cheers,
Brent
Intern
Joined: 16 Apr 2018
Posts: 16
Own Kudos [?]: 2 [0]
Given Kudos: 74
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
GMATPrepNow

I'm having difficulty in understanding the working of this question. By saying the slope is less, does that mean a slope of -1 is less than 1? I understand that one is positive and the other negative but the magnitude of the slope is equivalent and thus I would conclude that the slope is the same.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
Top Contributor
amandesai17 wrote:
GMATPrepNow

I'm having difficulty in understanding the working of this question. By saying the slope is less, does that mean a slope of -1 is less than 1? I understand that one is positive and the other negative but the magnitude of the slope is equivalent and thus I would conclude that the slope is the same.

Lines with slopes 1 and -1 have the same STEEPNESS, but the slopes are different.
So, the SLOPE of -1 is less than the SLOPE of 1

Cheers,
Brent
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5232
Own Kudos [?]: 4068 [4]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
2
Kudos
2
Bookmarks
nalinnair wrote:
In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Let line k be $$y-1 = m_1(x-1) => y=m_1x+(1-m_1)$$
Let line l be $$y-1 = m_2(x-1) => y =m_2x+(1-m_2)$$

Statement 1
$$m_1<m_2$$
$$=> 1-m_1>1-m_2$$
y intercept of k > y intercept of l
SUFFICIENT

Statement 2
m_2>0
NOT SUFFICIENT

IMO A
Intern
Joined: 24 Aug 2019
Posts: 9
Own Kudos [?]: 31 [2]
Given Kudos: 17
Location: United States (AK)
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
1
Kudos
1
Bookmarks
The equation of a line can be written as
$$y=mx+c$$
Since the 2 lines pass through (1,1), we can write this as
$$1=m+c$$
c is the y intercept as we get $$y=c$$ when $$x=0$$
Hence
$$c=1-m$$

(1) The slope of k is less than the slope of l.
Hence c will always be greater for k -Sufficient

2) The slope of l is positive.

A
Tutor
Joined: 16 Oct 2010
Posts: 14965
Own Kudos [?]: 65973 [8]
Given Kudos: 435
Location: Pune, India
Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]
4
Kudos
4
Bookmarks
nalinnair wrote:
In the xy-plane, lines k and l intersect at the point (1,1). Is the y-intercept of k greater than the y-intercept of l?

(1) The slope of k is less than the slope of l.
(2) The slope of l is positive.

Here are two posts that will help you understand the slope-intercept concept: