Jul 16 03:00 PM PDT  04:00 PM PDT Join a free live webinar and find out which skills will get you to the top, and what you can do to develop them. Save your spot today! Tuesday, July 16th at 3 pm PST Jul 16 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, July 16th at 8 pm EDT Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 09 Jul 2009
Posts: 42
Location: Bangalore
Schools: ISB

In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
Updated on: 13 Jun 2019, 03:48
Question Stats:
58% (01:31) correct 42% (01:55) wrong based on 1009 sessions
HideShow timer Statistics
In the xyplane, does the line with equation y = 3x + 2 contains the point (r,s)? (1) \((3r+2s)(4r+9s)=0\) (2) \((4r6s)(3r+2s)=0\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The only way of finding the limits of the possible is by going beyond them into the impossible.
Originally posted by gaurav2k101 on 04 Sep 2010, 06:35.
Last edited by Bunuel on 13 Jun 2019, 03:48, edited 2 times in total.
Updated.




Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
04 Sep 2010, 06:44
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 \(3r+2s=0\)) holds true. So basically we are asked to determine whether \(3r+2s=0\) is true or not. (1) \((3r+2s)(4r+9s)=0\) > either \(3r+2s=0\) OR \(4r+9s=0\) OR both. Not sufficient. (2) \((4r6s)(3r+2s)=0\) > either \(3r+2s=0\) OR \(4r6s=0\) OR both. Not sufficient. (1)+(2) Both \(4r+9s=0\) and \(4r6s=0\) cannot be true (simultaneously), as \(4rs\) can not equal to both 9 and 6, hence \(3r+2s=0\) must be true. Sufficient. Answer: C.
_________________




Manager
Joined: 09 Jun 2010
Posts: 100

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
04 Sep 2010, 07:19
Substituting (r,s) in the original equation: y=3x+2 => s=3r+2 => 3rs+2=0. Question : is 3rs2=0. ?? statement 1  (3r+2s)(4r+9s)=0 => (3r+2s)=0 or (4r+9s)=0 Not sufficient
Statement 2  (4r6s)(3r+2s)=0 => (3r+2s)=0 or (4r6s)=0 Not sufficient Combining 1&2 > common result (3r+2s)=0 Sufficient. Answer  C



Intern
Joined: 09 Jul 2009
Posts: 42
Location: Bangalore
Schools: ISB

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
04 Sep 2010, 08:50
I took it totally wrong: What i did was , from stmt 1: 1) (3r+2s)(4r+9s)=0 3r+2s=0 4r+9s=0 and equating both of them to find value of r and s. Total disaster. Thanks a lot guys ...Kudos to Bunuel and soumanag
_________________
The only way of finding the limits of the possible is by going beyond them into the impossible.



Manager
Joined: 16 Apr 2009
Posts: 243

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
05 Sep 2010, 09:55
Bunuel  you make every question looks so simple. always awesome explanation.
_________________



Manager
Joined: 20 Jul 2010
Posts: 205

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
10 Sep 2010, 10:55
awesome explanation Bunuel and Soumanag......thanks....
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them



Manager
Joined: 25 Jun 2010
Posts: 83

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
18 Dec 2010, 22:09
Quote: In the xy plane, does the line with equation y = 3x + 2 contain the point (r,s) ?
1. (3r + 2  s) (4r + 9  s) = 0
2. (4r 6 s) (3r + 2  s) = 0
y = 3x +2 will contain the point (r,s), if : s = 3r +2 (substitute r for x and s for y , in the eqn of line) => if 3r+2 s = 0 ? Statement 1 : (3r + 2  s) (4r + 9  s) = 0 => either (3r + 2 s) =0 or (4r +9 s ) = 0 > Not Sufficient Statement 2 : (4r 6 s) (3r + 2  s) = 0 => either (4r 6 s) = 0 or (3r + 2 s ) = 0 > Not sufficient Combining them : 3r + 2  s = 0  Sufficient (As [4r s +9] and [4r s 6] both can't be zero at the same time, they have a difference of 15). Hence , C.



Retired Moderator
Joined: 16 Nov 2010
Posts: 1360
Location: United States (IN)
Concentration: Strategy, Technology

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
09 Mar 2011, 22:05
s = 3r + 2 should be true if equation y = 3x+2 contain the point (r,s) From (1), s = 3r + 2 could be possible, but not sure because 4r + 9  s = 0 or 4r  s = 9 might be possible as well. From(2), s = 3r + 2 could be possible, but not sure because 4r  6  s = 0 or 4r  s = 6 might be possible as well. However, from (1) and (2), only 3r + 2  s = 0 can be true else 9 = 6, which is absurd. So the answer is C.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 79
Location: Pakistan
Concentration: International Business, Marketing
GPA: 3.2
WE: Business Development (Internet and New Media)

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
10 Jan 2012, 08:17
Ok.. So lets look at both the statements individually: First Statement 1: 1. (3r+2s)(4r+9s)=0 Look at the statement. It could mean two things. Either (3r+2s) = 0 or (4r+9s) = 0 if (3r+2s) = 0, then yes 3r+2s = 0 and hence s=3r+2 which is exactly like saying y=3x+2 But if 3r+2s is not equal to 0 then we don't know for sure. Now lets look at statement 2: 2. (4r6s)(3r+2s)=0 Same implies for statement 2. now lets assume that in the first statement 4r+9s=0. If that is true, then from the second statement it is not possible for 4r6s to be equal to 0. Hence 3r+2s = 0 and yes the point r,s which is the same as x,y lies on it ! Hence C
_________________
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde



Manager
Joined: 29 Jul 2011
Posts: 82
Location: United States

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
10 Jan 2012, 13:06
Easy one. GMAT loves these type of patterns. NOTE: Notice the pattern here. When you have similar type of information in both statements, the answer is usually C, D or E. 1. rephrasing the equations gives us s=3r+2 and s=4r+9. obviously s=4r+9 does not lie, but s=3r+2 does 2. rephrasing the equations gives us s=3r+2 and s=4r5. obviously s=4r5 does not lie, but s=3r+2 does Together, s=3r+2 and it does lie. C.
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



Intern
Joined: 16 Feb 2012
Posts: 7
Concentration: Entrepreneurship, General Management
GPA: 3.44
WE: General Management (Entertainment and Sports)

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
20 Apr 2012, 06:25
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 \(3r+2s=0\)) holds true.
So basically we are asked to determine whether \(3r+2s=0\) is true or not.
(1) \((3r+2s)(4r+9s)=0\) > either \(3r+2s=0\) OR \(4r+9s=0\) OR both. Not sufficient.
(2) \((4r6s)(3r+2s)=0\) > either \(3r+2s=0\) OR \(4r6s=0\) OR both. Not sufficient.
(1)+(2) Both \(4r+9s=0\) and \(4r6s=0\) can not be true (simultaneously), as \(4rs\) can not equal to both 9 and 6, hence \(3r+2s=0\) must be true. Sufficient.
Answer: C. Bunuel, Again, sorry for reopening an old thread but I have a small doubt regarding this question. I got this question on my GMAT Prep today, had one quick look at the options and immediately saw that for the point to lie on the line, 3r+2s has to be equal to zero. And since this information was given to us in two separate quadratic equations, it was necessary for us to have both the equations in order to discard (4r+9s) and (4r6s) as solutions to the given equations. However, at this point, I thought to myself that C would be too easy an answer and solved the equations to see if GMAT was upto its usual trickery. And this is where I went wrong. Take for example the first equation. One solution gives us what we want, i.e., 3r+2s = 0. However, if we solve the second solution 4r+9s = 0, we get s = 4r+9. Now, if we plug this into the original equation y = 3x+2, we get: y = 3x+2 Plugging the values of r and s into x and y: 4r+9 = 3r +2; Solving this gives us r = 7 and s = 19 and plugging these values of r and s in the original equation satisfies the equation: 19 = 3(7) + 2; 19 = 19 Since, this equation too satisfies the equation (and similarly, so does the second equation) I marked the answer as D. Can you please tell me where I am going wrong? Many thanks in advance.



Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
20 Apr 2012, 08:14
arjuntomar 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 \(3r+2s=0\)) holds true.
So basically we are asked to determine whether \(3r+2s=0\) is true or not.
(1) \((3r+2s)(4r+9s)=0\) > either \(3r+2s=0\) OR \(4r+9s=0\) OR both. Not sufficient.
(2) \((4r6s)(3r+2s)=0\) > either \(3r+2s=0\) OR \(4r6s=0\) OR both. Not sufficient.
(1)+(2) Both \(4r+9s=0\) and \(4r6s=0\) can not be true (simultaneously), as \(4rs\) can not equal to both 9 and 6, hence \(3r+2s=0\) must be true. Sufficient.
Answer: C. Bunuel, Again, sorry for reopening an old thread but I have a small doubt regarding this question. I got this question on my GMAT Prep today, had one quick look at the options and immediately saw that for the point to lie on the line, 3r+2s has to be equal to zero. And since this information was given to us in two separate quadratic equations, it was necessary for us to have both the equations in order to discard (4r+9s) and (4r6s) as solutions to the given equations. However, at this point, I thought to myself that C would be too easy an answer and solved the equations to see if GMAT was upto its usual trickery. And this is where I went wrong. Take for example the first equation. One solution gives us what we want, i.e., 3r+2s = 0. However, if we solve the second solution 4r+9s = 0, we get s = 4r+9. Now, if we plug this into the original equation y = 3x+2, we get: y = 3x+2 Plugging the values of r and s into x and y: 4r+9 = 3r +2; Solving this gives us r = 7 and s = 19 and plugging these values of r and s in the original equation satisfies the equation: 19 = 3(7) + 2; 19 = 19 Since, this equation too satisfies the equation (and similarly, so does the second equation) I marked the answer as D. Can you please tell me where I am going wrong? Many thanks in advance. The question asks whether \(3r+2s=0\). Now, statement (1) says: \((3r+2s)(4r+9s)=0\), which means that either \(3r+2s=0\) OR \(4r+9s=0\) OR both. The above DOES NOT mean that we have a system of equations: \(3r+2s=0\) and \(4r+9s=0\). Because if it were so then you have an answer right away: \(3r+2s=0\). No wonder that when you solve it as a system you got the values of \(s\) and \(r\) which make \(3r+2s\) equal to zero: your whole starting point was that it does. Hope it's clear.
_________________



Director
Joined: 14 Dec 2012
Posts: 739
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
08 Jul 2013, 03:59
gaurav2k101 wrote: In the xyplane , does the line with equation y=3x+2 contains the point(r,s)?
(1) (3r+2s)(4r+9s)=0 (2) (4r6s)(3r+2s)=0 A*B=0==>THEN EITHER A/B IS ZERO OR BOTH ARE ZERO...this is a rule. now if r,s lies on point y=3x+2==>then 3r+2s=0 now lets say 3r+2s=A.. 4r+9s=B 4r6s=C now statement 1 SAYS that ...A*B=0===>Clearly we are not sure that A=0 or not similarly statement 2 says that ...A*C===>AGAIN WE CANNOT GAURANTEE THAT A=0.. NOW combining both we cam clearly say that A=0.. HENCE SUFFICIENT.
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Manager
Joined: 11 Aug 2012
Posts: 114

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
30 Aug 2013, 15:41
Bunuel,
In statement (1), you have said that we have these possibilities: (3r + 2  s) = 0 OR (4r + 9  s) = 0 OR both.
But, when we have something like this: (x + 3)(x+5) = 0
In this case, there are only two possibilities, right? (x+3)=0 OR (x+5)=0. Both cannot be zero at the same time because "x" represents a single and unique value. Please confirm.



Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
31 Aug 2013, 06:13
danzig wrote: Bunuel,
In statement (1), you have said that we have these possibilities: (3r + 2  s) = 0 OR (4r + 9  s) = 0 OR both.
But, when we have something like this: (x + 3)(x+5) = 0
In this case, there are only two possibilities, right? (x+3)=0 OR (x+5)=0. Both cannot be zero at the same time because "x" represents a single and unique value. Please confirm. Yes. (3r + 2  s) = 0 and (4r + 9  s) = 0 can both be true, for r=7 and s=19. But for (x+3)=0 and (x+5)=0 both cannot be true simultaneously. Either x=3 or x=5. Hope it's clear.
_________________



Intern
Joined: 23 Aug 2014
Posts: 33
GMAT Date: 11292014

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
Updated on: 26 Nov 2014, 11:36
(Just so I get the whole picture) Say, instead of the bold parts in (3r+2s)(4r+9s)=0 and (4r6s)(3r+2s)=0, there are 2 slightly unrelated terms like 5r3s and 2r+7s.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
Joined: 02 Sep 2009
Posts: 56244

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
26 Nov 2014, 05:46
deeuk wrote: (Just so I get the whole picture) Say, instead of the bold parts in (3r+2s)(4r+9s)=0 and (4r6s)(3r+2s)=0, there were 2 slightly unrelated terms like 5r3s and 2r+7s, 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.
_________________



SVP
Joined: 06 Nov 2014
Posts: 1877

Re: In the xyplane, does the line with equation y = 3x + 2 contains the
[#permalink]
Show Tags
06 Jun 2016, 21:19
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



Director
Joined: 26 Oct 2016
Posts: 626
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: In the xyplane, 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: 3rs+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. (4rs = 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



NonHuman User
Joined: 09 Sep 2013
Posts: 11655

Re: In teh xy plane, does the line with equation y=3x+2 contain
[#permalink]
Show Tags
13 Jun 2019, 03:39
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 teh xy plane, does the line with equation y=3x+2 contain
[#permalink]
13 Jun 2019, 03:39






