 It is currently 19 Nov 2019, 06:49 ### 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, the point (1, 2) is on line j, and the poi  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Founder  Joined: 18 Apr 2015
Posts: 8780
Followers: 175

Kudos [?]: 2044  , given: 8096

In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
2
KUDOS
Expert's post 00:00

Question Stats: 63% (00:33) correct 36% (00:45) wrong based on 161 sessions

In the xy -plane, the point $$(1, 2)$$ is on line j, and the point $$(2, 1)$$ is on line k. Each of the lines has a positive slope.

 Quantity A Quantity B The slope of line $$j$$ The slope of line $$k$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Retired Moderator Joined: 07 Jun 2014
Posts: 4808
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2282  , given: 393

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
4
KUDOS
Expert's post
Explanation

Let us assume the line equations in terms of slope

line j: $$y = m1 \times x + c1$$ ....... has the point (1,2) on it.

line k: $$y = m2 \times x + c2$$ ....... has the point (2,1) on it.

Here m1 and m2 are slopes of the line j and k respectively.

Now putting the values (1,2) and (2,1) respectively into the equations of line j and k... we have

$$m1 + c1 = 2$$ and $$2 \times m2 + c2 = 1$$

Let m1 = 5 and m2 = 2 and solve for c1 and c2 from their respective equations

c1 = -3 and c2 = -3

Line j: $$y = 5 \times x -3$$
Line k: $$y = 2 \times x -3$$

Clearly slope m1 is greater.

Now let m1 = 2 and m2 = 5 and solve for c1 and c2 from their respective equations

c1 = 0 and c2 = -9

Line j: $$y = 2 \times x$$
Line k: $$y = 5 \times x -9$$

Clearly slope m2 is greater.

Hence option D is correct.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern Joined: 08 Apr 2018
Posts: 44
Followers: 0

Kudos [?]: 15 , given: 15

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
Carcass wrote:

In the xy -plane, the point (1, 2) is on line j, and the point (2, 1) is on line k. Each of the lines has a positive slope.

 Quantity A Quantity B The slope of line j The slope of line k

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Please can you throw more light on this solution? I drew the xy-graph and line J appeared to have a steeper slope hence making the slope larger, IMO. Why are we using the xy graph equation to solve this?
Retired Moderator Joined: 07 Jun 2014
Posts: 4808
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2282 , given: 393

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
Expert's post
Emike56 wrote:
Please can you throw more light on this solution? I drew the xy-graph and line J appeared to have a steeper slope hence making the slope larger, IMO. Why are we using the xy graph equation to solve this?

How did you draw the lines? Only one point on each line is given and nothing is mentioned about the slope. Essentially you can draw any line passing through either points as lonfg as the slope is positive!
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Intern Joined: 10 Sep 2018
Posts: 20
Followers: 0

Kudos [?]: 20  , given: 9

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
2
KUDOS
simply put, we are just given two points in the xy plane and are told that the lines have positive slopes. this means that they both represent increasing functions. nothing else is given. just from the info of two numbers being positive doesn't give any drawable conclusion as to their comparison.

had it said that the increasing rate of one function is greater or less than the other, then we could've drawn a conclusion. Intern Joined: 29 Jun 2018
Posts: 10
Followers: 0

Kudos [?]: 9  , given: 0

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
2
KUDOS
Easier way would be of think two different situations,

one is both the lines are parallel to x axis ie Slope is 0

and other take any random any position where the slope will differ.

SO D Director Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 45 , given: 1

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
Amit1997 wrote:
Easier way would be of think two different situations,

one is both the lines are parallel to x axis ie Slope is 0

and other take any random any position where the slope will differ.

SO D How are they become 0 ? Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 49  , given: 22

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
1
KUDOS
Expert's post
Right here, this problem doesn't require any calculation at all.
There are 2 separate lines, which are line k and line j
they both have a positive slope, and a point on each line.
But that's all the information we have.
In that case, we cant calculate the slope or each line, since we would need 2 points on the SAME LINE to do that, but we only have one point on each line, leaving us totally in the dark.
In this instance, we choose D. GRE Instructor Joined: 10 Apr 2015
Posts: 2569
Followers: 91

Kudos [?]: 2732  , given: 40

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
3
KUDOS
Expert's post
Carcass wrote:

In the xy -plane, the point $$(1, 2)$$ is on line j, and the point $$(2, 1)$$ is on line k. Each of the lines has a positive slope.

 Quantity A Quantity B The slope of line $$j$$ The slope of line $$k$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Here are some graphics to support what others have already said.

Knowing ONE point that that each line passes through doesn't help much.

For example, the two line could have the EXACT same slope. In this case, the two quantities are equal

Or it could be the case that line k has a steeper slope than line j In this case, Quantity B is greater

Or it could be the case that line j has a steeper slope than line k In this case, Quantity A is greater

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 24 May 2019
Posts: 28
Followers: 0

Kudos [?]: 18  , given: 0

Re: In the xy -plane, the point (1, 2) is on line j, and the poi [#permalink]
1
KUDOS
Carcass wrote:

In the xy -plane, the point $$(1, 2)$$ is on line j, and the point $$(2, 1)$$ is on line k. Each of the lines has a positive slope.

 Quantity A Quantity B The slope of line $$j$$ The slope of line $$k$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

---------CONCEPT NOTE-------------
There are infinite lines that can pass through a point.
So, we don't know which line the question is talking about when it mentions
A line passing through j (2,1)
& a line passing through k (1,2)

And hence answer is D as there are no fixed line even when slope is positive. Re: In the xy -plane, the point (1, 2) is on line j, and the poi   [#permalink] 01 Jun 2019, 03:33
Display posts from previous: Sort by

# In the xy -plane, the point (1, 2) is on line j, and the poi  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.