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

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

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

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Re: DS Question 2 [#permalink]

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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Re: DS Question 2 [#permalink]

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

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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Re: DS Question 2 [#permalink]

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

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