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Harish Dorai
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Post subject: In the XY plane, does the line with equation y = 3x + 2  Posted: Fri Aug 10, 2007 3:29 pm |
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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
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anadi
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Post subject: Lines Posted: Fri Aug 10, 2007 4:06 pm |
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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
In case 1, one of 2 brackets can be 0. If 3r+2-s = 0 then yes, line contains the point. Is 2nd bracket value is 0 , there is one valuse of r and s on which it does, but not for each value of r and s.
Same for case 2.
Coombined together, if both are true, 4r+9-s and 4r-6-S, can not both be 0 at the same time. So 3r+2-S = 0. This is same as y=3x+2. So if 3r+2-s = 0, this line will contain every (R,S) satisfying this equation.
So C is the answer. What is OA?
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Harish Dorai
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Post subject: Posted: Fri Aug 10, 2007 5:45 pm |
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(C) is the right answer. Great explanation!
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Guest
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Post subject: Posted: Fri Aug 08, 2008 8:51 pm |
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Could you please elaborate or clarify by what you mean when you say, "Combined together, if both are true, 4r+9-s and 4r-6-S, cannot both be 0 at the same time." Why is this so?
Thanks
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guest612
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Post subject: pls explain Posted: Wed Aug 13, 2008 3:39 pm |
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yes, can you please further explain the steps? for example, why are there only unique values for one of the brackets but not both for statements 1 & 2? also, isn't 3r+2-s a reiteration of the equation y=3x+2? but not sure how that answers the question and concludes that the line contains the coordinates (r,s). in sum, if you can just explain this a little more thoroughly it would be greatly appreciated! thanks.
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Guest813
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Post subject: Posted: Thu Aug 14, 2008 2:09 am |
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("4r-s"+9) and ("4r-s"-6) can not both be Zero...
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rfernandez
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Post subject: Posted: Fri Aug 22, 2008 3:35 am |
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| ManhattanGMAT Staff |
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Great solution, anadi. I'll give it a go, too.
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
Question: Does s = 3r + 2? Or, put another way, does 3r +2 - s = 0?
(1) Each of these factors may equal zero, so we know that either 3r + 2 - s = 0 OR that 4r + 9 - s = 0. Insufficient.
(2) Similarly, we know that either 4r - 6 - s = 0 OR that 3r + 2 - s = 0. Insufficient.
(1&2) The only possibility that would satisfy both statements is that 3r + 2 - s = 0. Sufficient.
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fighting_cax
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Post subject: Posted: Sat Jan 24, 2009 2:31 am |
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Hi Rey,
Just to clarify: how does finding out that 3r + 2 - s = 0 answer the question of whether y = 3x + 2 contain the point (r, s)?
Thanks.
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RonPurewal
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Post subject: Posted: Mon Jan 26, 2009 3:17 am |
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| ManhattanGMAT Staff |
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fighting_cax wrote: Hi Rey,
Just to clarify: how does finding out that 3r + 2 - s = 0 answer the question of whether y = 3x + 2 contain the point (r, s)?
Thanks.
the question of whether y = 3x + 2 contains (r, s) is the same as the question of whether s = 3r + 2. this is true of equations and graphs in general: "point (this, that) is on the graph of this equation" is the same as "when you plug this and that into the equation, the equation is true".
subtract s from both sides of 3r + 2 = s, giving 3r + 2 - s = 0. they're the same equation.
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amc08
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Post subject: Posted: Tue Feb 03, 2009 3:38 pm |
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cant we get 2 equations with 2 variables from (1) and then the values of r and s and see if it fits the equeation y= 3x+2 and the same we can do for (2) and then (1) and (2) are each sufficient and the answer is then D
??
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RonPurewal
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Post subject: Re: Posted: Wed Feb 18, 2009 6:29 am |
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| ManhattanGMAT Staff |
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amc08 wrote: cant we get 2 equations with 2 variables from (1) and then the values of r and s and see if it fits the equeation y= 3x+2 and the same we can do for (2) and then (1) and (2) are each sufficient and the answer is then D
?? no. the "two variables / two equations" approach only works when the equations are simultaneous: i.e., when they BOTH have to be true. this isn't the case here. if (3r + 2 - s)(4r + 9 - s) = 0, that means (3r + 2 - s) = 0 OR (4r + 9 - s) = 0. therefore, 3r - s = -2 OR 4r - s = -9, which has A LOT of solutions (anything that solves either of those equations qualifies as a solution). -- Quote: Could you please elaborate or clarify by what you mean when you say, "Combined together, if both are true, 4r+9-s and 4r-6-S, cannot both be 0 at the same time." Why is this so? 4r + 9 - s is (4r - 6 - s) plus 15. if some number is zero, then that number plus 15 isn't zero.
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itstimdy
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Post subject: Re: In the XY plane, does the line with equation y = 3x + 2 Posted: Tue Nov 15, 2011 12:37 am |
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Since the question asked if a point is on a line, I rephrased the question into, "Do we have enough information to find (r,s)?" Whether it falls on the line or not, it doesn't matter.
1) 1 equation 2 variables - NS
2) 1 equation 2 variables - NS
Together - after making sure they weren't the same equation, 2 variables 2 equations - S
Choice C.
I may have totally over simplified it.
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RonPurewal
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Post subject: Re: In the XY plane, does the line with equation y = 3x + 2 Posted: Wed Nov 23, 2011 6:36 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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itstimdy wrote: Since the question asked if a point is on a line, I rephrased the question into, "Do we have enough information to find (r,s)?" Whether it falls on the line or not, it doesn't matter.
1) 1 equation 2 variables - NS
2) 1 equation 2 variables - NS
Together - after making sure they weren't the same equation, 2 variables 2 equations - S
Choice C.
I may have totally over simplified it. yep, you totally oversimplified it. this is one of the few problems on which that kind of approach is a lucky guess -- it's usually a trap answer. for a half-hour or more on this problem -- including a couple of other variations that i made, on which the answer is not C -- watch the MARCH 17, 2011 lecture here: http://www.manhattangmat.com/thursdays-with-ron.cfm
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