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555-605 Level|   Coordinate Plane|                  
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 02 Aug 2018, 23:58
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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)
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C
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 17 Apr 2019, 23:29
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Bunuel
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.


NEW question from GMAT® Quantitative Review 2019


(DS13097)
Show more

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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If k and ℓ are lines in the xy-plane, is the slope of k less than the 03 Aug 2018, 02:27
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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
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 05 Aug 2018, 12:23
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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! :-)
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 18 Oct 2018, 09:14
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Bunuel
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.


NEW question from GMAT® Quantitative Review 2019


(DS13097)
Show more

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
Combined.png [ 39.73 KiB | Viewed 37432 times ]

File comment: This is one example of how many different ways we can get for statement 2
Statement 2.png
Statement 2.png [ 45.32 KiB | Viewed 37427 times ]

File comment: This is one example of how many different ways we can get for statement 1
Statement 1.png
Statement 1.png [ 37.38 KiB | Viewed 37395 times ]

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If k and ℓ are lines in the xy-plane, is the slope of k less than the 13 Apr 2019, 15:11
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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.

NEW question from GMAT® Quantitative Review 2019


(DS13097)[/quote]
Attachments

20190414_032153_Combining.jpg
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 36047 times ]

20190414_031608_Statement2.jpg
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 36016 times ]

20190414_030550_Statement1.jpg
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 36009 times ]

20190414_030550_Statement1.jpg
20190414_030550_Statement1.jpg [ 918.86 KiB | Viewed 36073 times ]

20190414_032153_Combining.jpg
20190414_032153_Combining.jpg [ 554.09 KiB | Viewed 35994 times ]

20190414_031608_Statement2.jpg
20190414_031608_Statement2.jpg [ 614.13 KiB | Viewed 35942 times ]

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If k and ℓ are lines in the xy-plane, is the slope of k less than the 18 Apr 2019, 03:00
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Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?

Posted from my mobile device
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 18 Apr 2019, 19:41
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Thanks
VeritasKarishma
for explaining the algebraic method.
What do you think of the graphical method that I explained earlier ?

Posted from my mobile device
Show more

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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If k and ℓ are lines in the xy-plane, is the slope of k less than the 04 Jul 2020, 01:11
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Bunuel
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.


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)
Show more




VeritasKarishma can you please explain more about the slope formula that you used? All I knew was Slope= Rise/Run
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If k and ℓ are lines in the xy-plane, is the slope of k less than the Updated on: 30 Nov 2023, 06:32
Originally posted by KarishmaB on 07 Jul 2020, 00:03.
Last edited by KarishmaB on 30 Nov 2023, 06:32, edited 1 time in total.
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VeritasKarishma
Bunuel
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.


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
Show more


Check here: https://anaprep.com/geometry-using-slop ... fectively/
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 01 Mar 2021, 17:50
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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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If k and ℓ are lines in the xy-plane, is the slope of k less than the 02 Mar 2021, 00:01
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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.
Show more

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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If k and ℓ are lines in the xy-plane, is the slope of k less than the 09 Nov 2022, 04:01
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Bunuel
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.


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)
Show more


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.
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 11 Nov 2022, 00:00
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KarishmaB
Bunuel
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.


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.
Show more


This is a generic formula for the slope of a line when the x intercept is not 0. Graph out a line and mark its y and x intercepts. The y and x intercepts give us two points on the line so the slope becomes defined. If the line passes through (0, 0), then both x and y intercepts are 0 and we get only one point and hence we cannot get the slope (mathematically, since x intercept is 0, we cannot use this expression)
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 24 Nov 2022, 02:44
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Bunuel KarishmaB
what does "k and l intersect on positive y-axis" mean?
is it that k's and l's y-intercept positive? or k's and l's intersection point has a positive y?
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If k and ℓ are lines in the xy-plane, is the slope of k less than the 24 Nov 2022, 02:54
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Bunuel KarishmaB
what does "k and l intersect on positive y-axis" mean?
is it that k's and l's y-intercept positive? or k's and l's intersection point has a positive y?
Show more

It means that their point of intersection lies on the positive Y axis.
So they intersect at a point such as (0, 3) or (0, 10) etc.
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