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# In the XY plane, does the line with equation Y=3X+2 contain

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Manager
Joined: 24 Sep 2008
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Schools: MIT / INSEAD / IIM - ABC
In the XY plane, does the line with equation Y=3X+2 contain [#permalink]

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24 Sep 2008, 18:10
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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
Intern
Joined: 21 Sep 2008
Posts: 16
Re: DS GMAT Prep CAT [#permalink]

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24 Sep 2008, 22:30
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

The question boils down to is s = 3r + 2 ?

From 1 we have s = 3r + 2 or s = 4r + 9
From 2 we have s = 4r + 6 or s = 3r + 2

so from 1 and 2 we have s = 3r + 2

Manager
Joined: 21 May 2008
Posts: 83
Re: DS GMAT Prep CAT [#permalink]

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24 Sep 2008, 23:19
From either (1) or (2), values of r and s can be obtained.
Therefore Ans is D.
Manager
Joined: 27 Aug 2008
Posts: 139
Re: DS GMAT Prep CAT [#permalink]

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25 Sep 2008, 04:26
GODSPEED wrote:
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

1) Either s= 3r+2 or s=4r+9

2) Either s=4r-6 or s=3r+2

Neither confirms s=3r+2 alone. But they do confirm when combined together. Hence Answer is C.
Intern
Joined: 03 Sep 2008
Posts: 22
Re: DS GMAT Prep CAT [#permalink]

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25 Sep 2008, 11:01
Question for those who say the answer is C. Is the answer still C if statment 2 is the following:

(3r-6-s)(3r+2-s)=0
SVP
Joined: 17 Jun 2008
Posts: 1507
Re: DS GMAT Prep CAT [#permalink]

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25 Sep 2008, 11:19
lsmv479 wrote:
Question for those who say the answer is C. Is the answer still C if statment 2 is the following:

(3r-6-s)(3r+2-s)=0

I would still go with C as C only gives a common solution of s = 2r + 3.
Manager
Joined: 24 Sep 2008
Posts: 185
Schools: MIT / INSEAD / IIM - ABC
Re: DS GMAT Prep CAT [#permalink]

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25 Sep 2008, 16:38
jahnaviyeruva wrote:
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

The question boils down to is s = 3r + 2 ?

From 1 we have s = 3r + 2 or s = 4r + 9
From 2 we have s = 4r + 6 or s = 3r + 2

so from 1 and 2 we have s = 3r + 2

OA is C......smart approach!!!
Intern
Joined: 03 Sep 2008
Posts: 22
Re: DS GMAT Prep CAT [#permalink]

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25 Sep 2008, 18:07
If the second statement is

(3r-6-s)(3r+2-s)=0

then the answer is not C. The points that satisfy 3r-s-6=0 line along a line as do the points that satisfy
4r+9-s=0. Since these lines do not have the same slope, they will have one point in common and that point will not be on the line Y=3x+2.

In the original problem the answer is C because both 4r+9-s=0 and 4r-6-s=0 have the same slope and therefore do not have a point in common. So both equations can only be true if s=3r+2
Manager
Joined: 24 Sep 2008
Posts: 185
Schools: MIT / INSEAD / IIM - ABC
Re: DS GMAT Prep CAT [#permalink]

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26 Sep 2008, 01:59
lsmv479 wrote:
If the second statement is

(3r-6-s)(3r+2-s)=0

then the answer is not C. The points that satisfy 3r-s-6=0 line along a line as do the points that satisfy
4r+9-s=0. Since these lines do not have the same slope, they will have one point in common and that point will not be on the line Y=3x+2.

In the original problem the answer is C because both 4r+9-s=0 and 4r-6-s=0 have the same slope and therefore do not have a point in common. So both equations can only be true if s=3r+2

Good Point

But it won't have changed the ANSWER choice, which is C [OA is C], because the solution to the two equations would be again the common line 3r+2-s=0 ans so C.

Am i wrong?? THINK
Re: DS GMAT Prep CAT   [#permalink] 26 Sep 2008, 01:59
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