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

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In the xy-plane, does the line with equation y=3x+2 contains [#permalink] New post 25 Nov 2007, 22:24
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In the xy-plane, does the line with equation y=3x+2 contains the point (r,s)?

(1) : (3r+2-s)(4r+9-s) = 0
(2) : (4r-6-s)(3r+2-s) = 0


Could someone, please, help me with this? This is from the official GMAT Prep Soft (Practice test 1). The solution was quite obvious to me, but the OA surprized me.
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Re: DS - the point and the line [#permalink] New post 25 Nov 2007, 22:59
don17 wrote:
In the xy-plane, does the line with equation y=3x+2 contains the point (r,s)?

(1) : (3r+2-s)(4r+9-s) = 0
(2) : (4r-6-s)(3r+2-s) = 0


Could someone, please, help me with this? This is from the official GMAT Prep Soft (Practice test 1). The solution was quite obvious to me, but the OA surprized me.


Ya C.

Dont try to multiply that behemoth out. Just realize that S1: is s=3r+2

and S2: also has s=3r+2. Combined we know that s=3r+2

Suff.
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Re: DS - the point and the line [#permalink] New post 25 Nov 2007, 23:06
GMATBLACKBELT wrote:
don17 wrote:
In the xy-plane, does the line with equation y=3x+2 contains the point (r,s)?

(1) : (3r+2-s)(4r+9-s) = 0
(2) : (4r-6-s)(3r+2-s) = 0


Could someone, please, help me with this? This is from the official GMAT Prep Soft (Practice test 1). The solution was quite obvious to me, but the OA surprized me.


Ya C.

Dont try to multiply that behemoth out. Just realize that S1: is s=3r+2

and S2: also has s=3r+2. Combined we know that s=3r+2

Suff.


Sorry, could you please explain it in more details.

We have 3r+2-s, which gives us s=3r+2 in each of the conditions. I thought this means that each is suff. Thus D. Why C then?
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Re: DS - the point and the line [#permalink] New post 25 Nov 2007, 23:33
walker wrote:
GMATBLACKBELT wrote:
Just realize that S1: is s=3r+2
and S2: also has s=3r+2. Combined we know that s=3r+2

Suff.


Exactly.


But why we do not know this from S1 only, or from S2 only? What for we need this 2 conditions together?
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 [#permalink] New post 25 Nov 2007, 23:40
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For example, first statement

(3r+2-s)(4r+9-s)=0 ==> (3r+2-s)=0 (very good) or (4r+9-s)

Therefore, all r,s from (3r+2-s)=0 match y=3x+2, but r,s from (4r+9-s)=0 - no. INSUFF.

1&2. means (3r+2-s)=0. because no any r,s that satisfies both (4r+9-s)=0 and (4r-6-s)=0 (these lines are parallel and do not intersect) - SUFF
  [#permalink] 25 Nov 2007, 23:40
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