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If k and ℓ are lines in the xy-plane, is the slope of k less than the
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02 Aug 2018, 22:58
02 Aug 2018, 22:58
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If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
_________________
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
_________________
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
17 Apr 2019, 22:29
17 Apr 2019, 22:29
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Expert Reply
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
NEW question from GMAT® Quantitative Review 2019
(DS13097)
Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept)
Is slopek < slopel ?
Is - yk / xk < - yl / xl ?
Is yk / xk > yl / xl ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
xk > 0
xl < 0
Since we don't know anything about yk and yl, this is not sufficient.
(2) Lines k and ℓ intersect on the positive y-axis.
This means both yk and yl are positive. But we don't know anything about xk and xl.
Using both, yk/xk is positive because both yk and xk are positive.
yl/xl is negative because yl is positive but xl is negative.
Then, yk / xk is certainly greater than yl / xl.
Sufficient. Answer (C)
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
03 Aug 2018, 01:27
03 Aug 2018, 01:27
15
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14
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Expert Reply
To find if the slope of k less than the slope of ℓ
Statement 1
The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
Case 1
K can have a +ve slope when k rises upward while running from left to right and ℓ can have a -ve slope when ℓ slides downward while running from left to right
=> slope of line k > slope of line ℓ
Case 2
K can have a -ve slope when k slides downwards while running from left to right and ℓ can have a +ve slope when ℓ rises upward while running from left to right
=> slope of line k < slope of line ℓ
Statement 1 is not sufficient
Statement 2
Lines k and ℓ intersect on the positive y-axis. Both the above mentioned cases are still possible
Statement 2 is not sufficient
Combining statements 1 and 2
Since x-intercept of line k is positive and y-intercept of line k is positive => K has negative slope
Since x-intercept of line ℓ is negative and y-intercept of line ℓ is positive => ℓ has positive slope
=> slope of line ℓ > slope of line k
Statements 1 and 2 together are sufficient
Hence option C
_________________
Statement 1
The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
Case 1
K can have a +ve slope when k rises upward while running from left to right and ℓ can have a -ve slope when ℓ slides downward while running from left to right
=> slope of line k > slope of line ℓ
Case 2
K can have a -ve slope when k slides downwards while running from left to right and ℓ can have a +ve slope when ℓ rises upward while running from left to right
=> slope of line k < slope of line ℓ
Statement 1 is not sufficient
Statement 2
Lines k and ℓ intersect on the positive y-axis. Both the above mentioned cases are still possible
Statement 2 is not sufficient
Combining statements 1 and 2
Since x-intercept of line k is positive and y-intercept of line k is positive => K has negative slope
Since x-intercept of line ℓ is negative and y-intercept of line ℓ is positive => ℓ has positive slope
=> slope of line ℓ > slope of line k
Statements 1 and 2 together are sufficient
Hence option C
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General Discussion
IIM School Moderator
Joined: 17 Aug 2015
Posts: 113
Location: India
GMAT 1: 690 Q48 V36 
GPA: 4
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
05 Aug 2018, 11:23
05 Aug 2018, 11:23
6
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1
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Equation: y=mx+c
Case 1 for line k: x intercept is -c/m>0
Case 1 for line l: x intercept is -c/m<0
Statement 1 is not Sufficient as in both the cases, either c could be -ve or m could be -ve
Case 2: Y intercept is positive => c is positive in the equation for both lines
Statement 2 is not Sufficient as in both the cases, slope information is not there
Combining
Case 1 for line k: x intercept is -c/m>0 , given c >0 , m is -ve
Case 1 for line l: x intercept is -c/m<0, given c>0, m is +ve
=> slope l>slope k or slope k<slope l - Sufficient
C
Hope this helps!
Case 1 for line k: x intercept is -c/m>0
Case 1 for line l: x intercept is -c/m<0
Statement 1 is not Sufficient as in both the cases, either c could be -ve or m could be -ve
Case 2: Y intercept is positive => c is positive in the equation for both lines
Statement 2 is not Sufficient as in both the cases, slope information is not there
Combining
Case 1 for line k: x intercept is -c/m>0 , given c >0 , m is -ve
Case 1 for line l: x intercept is -c/m<0, given c>0, m is +ve
=> slope l>slope k or slope k<slope l - Sufficient
C
Hope this helps!
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Posts: 416
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
18 Oct 2018, 08:14
18 Oct 2018, 08:14
1
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1
Bookmarks
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
NEW question from GMAT® Quantitative Review 2019
(DS13097)
Best way to solve it is to draw
Refer to the drawings to have an idea of how I solved it.
answer choice C
Attachments
File comment: This is how it can be solved if combined
Combined.png [ 39.73 KiB | Viewed 33986 times ]
File comment: This is one example of how many different ways we can get for statement 2
Statement 2.png [ 45.32 KiB | Viewed 33981 times ]
File comment: This is one example of how many different ways we can get for statement 1
Statement 1.png [ 37.38 KiB | Viewed 33942 times ]
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
13 Apr 2019, 14:11
13 Apr 2019, 14:11
7
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5
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@Bunuel
@VeritasKarishma
@Chetan2u
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
Statement 1 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.
(2) Lines k and ℓ intersect on the positive y-axis.
Statement 2 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.
Combining it's sufficient as it leads to only one possibility i.e SLope of L is greater than slope of K.
Answer is option C.
I have attached three images in support of my explanation.
Please find them attached herewith.
Please Please give me kudos if you found my explanation helpful.
(DS13097)[/quote]
@VeritasKarishma
@Chetan2u
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
Statement 1 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.
(2) Lines k and ℓ intersect on the positive y-axis.
Statement 2 is not sufficient as it can lead to both possibilities .
SLope of L can be greater than that of K or slope of K can be greater than that of L.
Combining it's sufficient as it leads to only one possibility i.e SLope of L is greater than slope of K.
Answer is option C.
I have attached three images in support of my explanation.
Please find them attached herewith.
Please Please give me kudos if you found my explanation helpful.
NEW question from GMAT® Quantitative Review 2019
(DS13097)[/quote]
Attachments
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 32645 times ]
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 32604 times ]
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 32599 times ]
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 32667 times ]
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 32591 times ]
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 32545 times ]
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
18 Apr 2019, 02:00
18 Apr 2019, 02:00
Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?
Posted from my mobile device
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?
Posted from my mobile device
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
18 Apr 2019, 18:41
18 Apr 2019, 18:41
2
Kudos
Expert Reply
sayan640 wrote:
Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?
Posted from my mobile device
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?
Posted from my mobile device
Sayan60,
Certainly there is nothing wrong with graphing out the question and I am a big proponent of making diagrams etc. Just that with multiple lines and slopes and various constraints given in the statements, I find it a bit confusing and worry about missing a case or two. So I have found that the slope and intercept method I discussed above is far more efficient in these cases.
_________________
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
04 Jul 2020, 00:11
04 Jul 2020, 00:11
VeritasKarishma wrote:
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
NEW question from GMAT® Quantitative Review 2019
(DS13097)
Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept)
Is slopek < slopel ?
Is - yk / xk < - yl / xl ?
Is yk / xk > yl / xl ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
xk > 0
xl < 0
Since we don't know anything about yk and yl, this is not sufficient.
(2) Lines k and ℓ intersect on the positive y-axis.
This means both yk and yl are positive. But we don't know anything about xk and xl.
Using both, yk/xk is positive because both yk and xk are positive.
yl/xl is negative because yl is positive but xl is negative.
Then, yk / xk is certainly greater than yl / xl.
Sufficient. Answer (C)
VeritasKarishma can you please explain more about the slope formula that you used? All I knew was Slope= Rise/Run
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
06 Jul 2020, 23:03
06 Jul 2020, 23:03
1
Bookmarks
Expert Reply
Dpkkukreja wrote:
VeritasKarishma wrote:
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
NEW question from GMAT® Quantitative Review 2019
(DS13097)
Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept)
Is slopek < slopel ?
Is - yk / xk < - yl / xl ?
Is yk / xk > yl / xl ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
xk > 0
xl < 0
Since we don't know anything about yk and yl, this is not sufficient.
(2) Lines k and ℓ intersect on the positive y-axis.
This means both yk and yl are positive. But we don't know anything about xk and xl.
Using both, yk/xk is positive because both yk and xk are positive.
yl/xl is negative because yl is positive but xl is negative.
Then, yk / xk is certainly greater than yl / xl.
Sufficient. Answer (C)
VeritasKarishma can you please explain more about the slope formula that you used? All I knew was Slope= Rise/Run
Check here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -vertices/
_________________
Karishma Bansal - ANA PREP
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
08 Nov 2020, 17:33
08 Nov 2020, 17:33
I think for these questions it's best to draw them out in order to visualize the scenarios:
_________________
Attachments
kandl.png [ 14.68 KiB | Viewed 22705 times ]
_________________
Help me get better -- please critique my responses!
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
01 Mar 2021, 16:50
01 Mar 2021, 16:50
Might be a silly question, but suppose you have two negative slopes and one of them is more negative than the other. Is it always the case that the more positive slope is larger? Or can the more negative one be 'steeper'? Maybe I got it twisted.
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
01 Mar 2021, 23:01
01 Mar 2021, 23:01
1
Kudos
Expert Reply
CEdward wrote:
Might be a silly question, but suppose you have two negative slopes and one of them is more negative than the other. Is it always the case that the more positive slope is larger? Or can the more negative one be 'steeper'? Maybe I got it twisted.
A steeper incline indicates a higher absolute value of the slope.
So, if both lines have positive slopes, then the line which is steeper has greater slope.
If both lines have negative slopes, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line.
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
31 Jan 2022, 09:28
31 Jan 2022, 09:28
i thought that sign of slope does not matter as it does not represent steepness while absolute value of slope does. Since absolute value of slope of lines k and l can be different, i concluded that it is impossible to find out which line is stepper. Where did i make mistake during this thought analysis ?
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
31 Jan 2022, 21:54
31 Jan 2022, 21:54
agobbo30 wrote:
Does Statement 2 indicate the the Y-intercept of both lines is positive?
I interpreted it as the two lines crossing each other somewhere where the y coordinate is positive (quadrant 1 or 2) but clearly that is not the proper understanding.
I interpreted it as the two lines crossing each other somewhere where the y coordinate is positive (quadrant 1 or 2) but clearly that is not the proper understanding.
Statement 2 says they intersect "on positive y axis"
the lines K and L intersect on the positive Y axis(the positive number line on Y)
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
31 Jan 2022, 22:05
31 Jan 2022, 22:05
1
Bookmarks
Vesper2018 wrote:
i thought that sign of slope does not matter as it does not represent steepness while absolute value of slope does. Since absolute value of slope of lines k and l can be different, i concluded that it is impossible to find out which line is stepper. Where did i make mistake during this thought analysis ?
no, the signs do matter.
say there are two lines A and B with slopes of -5 and 2 respectively.
the slope of line A is definitely lesser than that of line B.
here, the difference in slopes is the same as comparing which value (-5 or 2) is greater, and not the absolute values of the slopes.
if both lines have positive slopes, the steeper slope is the larger value
if both lines have negative slopes, the steeper slope(larger negative value) will be considered as the lesser/smaller slope.
for eg:
2 lines have slopes -3 and -10.
the line with -10 slope is steeper but it has a larger negative value than -3.
thus the line with slope -3 has larger slope as compared to the line with -10.
you can also compare them by taking the values of angles made by the lines with the x axis in counter-clockwise direction.
the larger the angle, the higher/greater is the slope for that line.
you can try it out by sketching a few figures.
i hope i was helpful.
thank you (:
Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the
[#permalink]
07 Feb 2022, 04:06
07 Feb 2022, 04:06
Bunuel could you attach similar links to this thread? Would like to practice a few of such question types
Re: If k and are lines in the xy-plane, is the slope of k less than the
[#permalink]
02 Jul 2022, 03:04
02 Jul 2022, 03:04
Bunuel wrote:
CEdward wrote:
Might be a silly question, but suppose you have two negative slopes and one of them is more negative than the other. Is it always the case that the more positive slope is larger? Or can the more negative one be 'steeper'? Maybe I got it twisted.
A steeper incline indicates a higher absolute value of the slope.
So, if both lines have positive slopes, then the line which is steeper has greater slope.
If both lines have negative slopes, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line.
Bunuel
What is about a positive slopes and a negative slope?
For example,
1) m1 = 2, m2 = -2 which m1 or m2 is greater
2) m1 = 3, m2 = -5 which m1 or m2 is greater
Re: If k and are lines in the xy-plane, is the slope of k less than the
[#permalink]
02 Jul 2022, 03:20
02 Jul 2022, 03:20
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
combine statement 1 and 2, we know that The slope of L is positive and that of K is negative.
But we don't know the absolute value of slope L & K. How we actually know that The slope of L > that of K.
The more absolute value of a slope, the more steepness of the Line. Thus, if we don't know absolute value, we cannot conclude that which is greater.
Could anyone elaborate why C is correct?
Re: If k and are lines in the xy-plane, is the slope of k less than the
[#permalink]
09 Nov 2022, 03:01
09 Nov 2022, 03:01
KarishmaB wrote:
Bunuel wrote:
If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
(DS13097)
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.
NEW question from GMAT® Quantitative Review 2019
(DS13097)
Relation between slope and intercepts of a line: Slope of a line = – (y intercept)/(x intercept)
Is slopek < slopel ?
Is - yk / xk < - yl / xl ?
Is yk / xk > yl / xl ?
(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
xk > 0
xl < 0
Since we don't know anything about yk and yl, this is not sufficient.
(2) Lines k and ℓ intersect on the positive y-axis.
This means both yk and yl are positive. But we don't know anything about xk and xl.
Using both, yk/xk is positive because both yk and xk are positive.
yl/xl is negative because yl is positive but xl is negative.
Then, yk / xk is certainly greater than yl / xl.
Sufficient. Answer (C)
Hello KarishmaB Ma'am,
Can we use the below formula anywhere or are there any constraints?
Slope of a line = – (y intercept)/(x intercept)
Thank you for your time.
gmatclubot
Re: If k and are lines in the xy-plane, is the slope of k less than the [#permalink]
09 Nov 2022, 03:01
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