It is currently 18 Oct 2017, 02:34

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the xy-plane , does the line with equation y = 3x + 2 contains the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Aug 2014
Posts: 42

Kudos [?]: 10 [0], given: 28

GMAT Date: 11-29-2014
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

25 Nov 2014, 12:28
(Just so I get the whole picture) Say, instead of the bold parts in (3r+2-s)(4r+9-s)=0 and (4r-6-s)(3r+2-s)=0, there are 2 slightly unrelated terms like 5r-3-s and 2r+7-s.They would remain to be possibilities of the equation and E would be the right choice, right?
Sorry if I am complicating things.

Last edited by deeuk on 26 Nov 2014, 11:36, edited 1 time in total.

Kudos [?]: 10 [0], given: 28

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [1], given: 12181

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

26 Nov 2014, 05:46
1
KUDOS
Expert's post
deeuk wrote:
(Just so I get the whole picture) Say, instead of the bold parts in (3r+2-s)(4r+9-s)=0 and (4r-6-s)(3r+2-s)=0, there were 2 slightly unrelated terms like 5r-3-s and 2r+7-s, they would remain to be possibilities of the equation and E would be the right choice, right?
Sorry if I am complicating things.

Yes, in this case the answer would be E.
_________________

Kudos [?]: 128668 [1], given: 12181

Manager
Joined: 14 Mar 2014
Posts: 150

Kudos [?]: 166 [0], given: 124

GMAT 1: 710 Q50 V34
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

02 Aug 2015, 03:24
visram04 wrote:
In the xy plane, does the line y=3x+2 contain the point (r,s)?
i) (3r+2-s)(4r+9-s)=0
ii) (4r-6-s)(3r+2-s)=0

Question Stem: If Point (r,s) lies on the line y =3x+2, then the point should satisfy the equation, i.e., s=3r+2

St 1: (3r+2-s)(4r+9-s)=0

3r+2 = s or 4r+9 =s
We dont have unique solution. Hence not sufficient

St 2: (4r-6-s)(3r+2-s)=0

4r-6 = s or 3r+2 = s
We dont have unique solution. Hence not sufficient

Combined:

Combining we get s = 3r+2 --> which is required to prove from the question stem.
Hence sufficient.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯

Kudos [?]: 166 [0], given: 124

Intern
Joined: 05 Jul 2014
Posts: 7

Kudos [?]: [0], given: 38

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

22 Mar 2016, 04:32
gaurav2k101 wrote:
In the xy-plane , does the line with equation y=3x+2 contains the point(r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

I did it differently, but it could be totally wrong. It would be good if someone can check it. Bunuel I would highly appreciate it if you check it.

I substituted 0 for r for both statements,

(1) (3(0)+2-s)(4(0)+9-s)=0 so that s=2 (which is on the line) or 9 (which is not on the line)

(2) (4(0)-6-s)(3(0)+2-s)=0 so that s=6 (which is not on the line) or 2 (which is on the line)

Alone statement 1 and 2 are insufficient since they could be either 1 of 2 values, but together they prove that s=2, so the answer is C.

Kudos [?]: [0], given: 38

Optimus Prep Instructor
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 522 [1], given: 23

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

06 Jun 2016, 21:19
1
KUDOS
Expert's post
Required: Does the line with equation y=3*X +2 contain the point (r,s)
Or simply put, Is 3r - s +2 = 0?

Statement 1: (3r + 2 - s)(4r + 9 - s) = 0
This means either
(3r + 2 - s) = 0
Or (4r + 9 - s) = 0
INSUFFICIENT

Statement 2: (4r - 6 - s)(3r + 2 - s) = 0
This means either
(4r - 6 - s) = 0
Or (3r + 2 - s) = 0
INSUFFICIENT

Combining both statements:
We know that (3r + 2 - s) = 0
SUFFICIENT

Correct Option: C
_________________

# Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring GMAT On Demand Course$299
Free Online Trial Hour

Kudos [?]: 522 [1], given: 23

Manager
Joined: 13 Jun 2016
Posts: 135

Kudos [?]: 120 [0], given: 424

Location: United States
Concentration: Finance, Technology
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

05 Aug 2016, 10:07
Substituting variables r and s for x and y is very smart. Then the question becomes a logic question.

(1) can contain the point or it could not
(2) can contain the point or could not (just like statement 1)

Together at first it looks like it will not work out, however it has to have the point because the other two equations could not satisfy both of the equations. It would be 4r + 9 = 4r - 6 which would never work.

Kudos [?]: 120 [0], given: 424

Intern
Joined: 15 Aug 2016
Posts: 3

Kudos [?]: [0], given: 2

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

20 Aug 2016, 10:25
1
This post was
BOOKMARKED
Guys, please say if I am wrong.
If the question was found that
1) (3r+3-s) (4r+9-s)=0
2) (4r-6-s) (3r+3-s)=0
then we will conclud that the answer is C, do not contain since parallel

If the question was found that
1) (4r+2-s) (4r+9-s)=0
2) (4r-6-s) (4r+2-s)=0
then we will conclud that the answer is C, contain since intercept

am I right?

Kudos [?]: [0], given: 2

Director
Joined: 26 Oct 2016
Posts: 694

Kudos [?]: 179 [0], given: 855

Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

30 Jan 2017, 18:24
(r,s) will lie on the line with equation y = 3x + 2, if in place of x and y respectively we put the coordinates of the point and the line equation is satisfied.

So , (r,s) will lie on y = 3x +2, if s=3r+2 or in other words:

3r-s+2 = 0.

From St. 1:

(3r + 2 - s)(4r + 9 - s) = 0
i.e.

either

(3r + 2 - s) = 0 or (4r + 9 - s) = 0.

Say (3r + 2 - s) = 0 -->St. 1 satisfied and (r, s) lies on given line.

Now say, (3r + 2 - s) not equal to zero, but
(4r + 9 - s) = 0

Then St. 1 satisfied but (r, s) does not lie on given line.

So St. 1 is not sufficient.

Exactly same logic for St. 2.

St. 2 not sufficient.

Combining both statements.

case 1: (3r + 2 - s) is equal to zero

case 2: (3r + 2 - s) is not equal to zero

let's discuss case (2):

This means that

(4r + 9 - s) = 0 and also (4r - 6 - s) = 0

which is absurd. (4r-s = -9 as well as 6--> not possible)

so only case 1 holds i.e.

(3r + 2 - s) is equal to zero

_________________

Thanks & Regards,
Anaira Mitch

Kudos [?]: 179 [0], given: 855

Intern
Joined: 25 Jan 2017
Posts: 1

Kudos [?]: 0 [0], given: 18

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

01 Feb 2017, 07:33
Bunuel wrote:
In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ cannot be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

Hi,

This solution will not hold true if r and s are on a rotated axis on the plane i.e. r= xcosA + ysinA and s = -xsinA + ycosA for any A. In this case line representing 3r+2-s=0 will intersect 3x+2 = y at a single point, thus the line 3x+2 = y may or may not contain (r,s), hence, E.

Kudos [?]: 0 [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [0], given: 12181

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the [#permalink]

### Show Tags

01 Feb 2017, 08:06
Kapidhwaj wrote:
Bunuel wrote:
In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ cannot be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

Hi,

This solution will not hold true if r and s are on a rotated axis on the plane i.e. r= xcosA + ysinA and s = -xsinA + ycosA for any A. In this case line representing 3r+2-s=0 will intersect 3x+2 = y at a single point, thus the line 3x+2 = y may or may not contain (r,s), hence, E.

Dear Kapidhwaj,

Not sure what are you trying to say but the only solution (3r+2-s)(4r+9-s)=0 and (4r-6-s)(3r+2-s)=0 has is 3r+2-s=0, which makes the answer C correct. Also, note that this is an official question and confirmed OA is C.
_________________

Kudos [?]: 128668 [0], given: 12181

Re: In the xy-plane , does the line with equation y = 3x + 2 contains the   [#permalink] 01 Feb 2017, 08:06

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by