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

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

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New post 12 May 2009, 17:34
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In xy-plane, does 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

Kudos [?]: 6 [0], given: 2

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SVP
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Joined: 07 Nov 2007
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Location: New York
Re: DS Question 2 [#permalink]

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New post 12 May 2009, 19:58
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meesawoosa wrote:
In xy-plane, does 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



rewrite the question stem:
Is s=3r+2 ? (i.e 3r-s+2=0?)


1) (3r +2-s)(4r+9-s)=0
either (3r +2-s) =0 or (4r+9-s)=0 or both=0

not sufficient

2) (4r-6-s)(3r+2-s)=0
either (3r +2-s) =0 or (4r-6-s)=0 or both=0


combined
assume that (4r+9-s)=0 then (4r-6-s) definitely <>0 so (3r +2-s) =0 must satisfy.


C is the answer.
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Kudos [?]: 1088 [1], given: 5

Director
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Re: DS Question 2 [#permalink]

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New post 12 May 2009, 21:47
x2suresh wrote:
meesawoosa wrote:
In xy-plane, does 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



rewrite the question stem:
Is s=3r+2 ? (i.e 3r-s+2=0?)


1) (3r +2-s)(4r+9-s)=0
either (3r +2-s) =0 or (4r+9-s)=0 or both=0

not sufficient

2) (4r-6-s)(3r+2-s)=0
either (3r +2-s) =0 or (4r-6-s)=0 or both=0


combined
assume that (4r+9-s)=0 then (4r-6-s) definitely <>0 so (3r +2-s) =0 must satisfy.
C is the answer.


i found both statements insufficient but couldnt see how the answer could be C

can you elaborate on C? I dont really understand your rationalization

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Manager
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Re: DS Question 2 [#permalink]

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New post 14 May 2009, 13:52
meesawoosa wrote:
In xy-plane, does line with equation y = 3x+2 contain the point (r,s)?

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

2. \((4r-6-s)(3r+2-s)=0\)


If (r,s) is on the line y=3x+2, then we can substitute in y=s & x=r into the equation to get,
Question:(\(s=3r+2\))?
Question:(\(3r+2-s=0\))?

(1) \((3r +2-s)(4r+9-s)=0\)
This implies that either \(3r+2-s=0\) or \(4r+9-s=0\), the first equation gives us a YES, the second one a NO. Insufficient.

(2) \((4r-6-s)(3r+2-s)=0\)
This implies that either \(4r-6-s=0\) or \(3r+2-s=0\), the first equation gives us a YES, the second one a NO. Insufficient.

(1&2) Combining the facts above gives us
\(3+2-s=0\) OR \(4r+9-s=0\)
AND
\(4r-6-s=0\) OR \(3r+2-s=0\)

This implies that \(3r+2-s=0\) is true, what we're trying to find.

Final Answer, C.
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Re: DS Question 2   [#permalink] 14 May 2009, 13:52
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In xy-plane, does line with equation y = 3x+2 contain the

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