GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 May 2019, 22:34 ### 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
Your Progress

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 23 Aug 2014
Posts: 34
GMAT Date: 11-29-2014
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

(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.

Originally posted by deeuk on 25 Nov 2014, 12:28.
Last edited by deeuk on 26 Nov 2014, 11:36, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 55231
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

1
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.
_________________
Manager  B
Joined: 14 Mar 2014
Posts: 147
GMAT 1: 710 Q50 V34 Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

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)_/¯ Intern  Joined: 05 Jul 2014
Posts: 6
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

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.
SVP  B
Joined: 06 Nov 2014
Posts: 1877
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

1
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
Manager  Joined: 13 Jun 2016
Posts: 105
Location: United States
Concentration: Finance, Technology
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

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.
Intern  Joined: 15 Aug 2016
Posts: 3
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

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?
Director  G
Joined: 26 Oct 2016
Posts: 633
Location: United States
Concentration: Marketing, International Business
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

(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

(C) is the answer.
_________________
Thanks & Regards,
Anaira Mitch
Non-Human User Joined: 09 Sep 2013
Posts: 10980
Re: In the xy-plane , does the line with equation y = 3x + 2 contains the  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: In the xy-plane , does the line with equation y = 3x + 2 contains the   [#permalink] 26 Nov 2018, 12:04

Go to page   Previous    1   2   [ 29 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  