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GMAT PREP DS

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by sykedaddy » Fri Jul 06, 2007 4:01 pm
In the xy- plane, does the line with equation y=3x + 2 contain point (r,s)?

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

I say that they equal each other....but get stuck going down that road...no variables...
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Source: — Data Sufficiency |
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by givemeanid » Fri Jul 06, 2007 4:16 pm
Does y=3x + 2 contain point (r,s)?
In other words, is s = 3r + 2.
Rearranging the equations, the question is whether 3r + 2 - s = 0?

(1) (3r+2-s)(4r+9-s) = 0
So, either 3r+2-s = 0 or 4r+9-s = 0
NOT SUFFICIENT.

(2) (4r-6-s) (3r+2-s) = 0
So, either 4r-6-s = 0 or 3r+2-s = 0
NOT SUFFICIENT.

Combining both, 3r+2-s = 0.
SUFFICIENT.


Answer is (C).
So It Goes
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by eby_98 » Thu Jul 12, 2007 6:46 pm
Is (c) the correct answer?
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Re: GMAT PREP DS

by gabriel » Fri Jul 13, 2007 4:25 am
sykedaddy wrote:In the xy- plane, does the line with equation y=3x + 2 contain point (r,s)?

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

I say that they equal each other....but get stuck going down that road...no variables...
DS questions go in the DS section :( ...
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by sykedaddy » Mon Jul 16, 2007 6:18 am
Sorry...yes ans. is C
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by bingojohn » Wed Aug 08, 2007 5:06 am
givemeanid wrote:Does y=3x + 2 contain point (r,s)?
In other words, is s = 3r + 2.
Rearranging the equations, the question is whether 3r + 2 - s = 0?

(1) (3r+2-s)(4r+9-s) = 0
So, either 3r+2-s = 0 or 4r+9-s = 0
NOT SUFFICIENT.

(2) (4r-6-s) (3r+2-s) = 0
So, either 4r-6-s = 0 or 3r+2-s = 0
NOT SUFFICIENT.

Combining both, 3r+2-s = 0.
SUFFICIENT.


Answer is (C).
What does the emphasized text above mean. In other words how do you combine the two equations to arrive at 3r + 2 - s = 0, definitively? Please explain.
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by givemeanid » Wed Aug 08, 2007 7:18 am
3r+2-s = 0 is the only condition that is satisfied by BOTH 1 and 2.
So It Goes
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by Patrick_GMATFix » Fri May 21, 2010 10:45 am
The explanation below is pasted from a different thread

the Q tests your understanding that point (r,s) can belong to the line only if its coordinates fit the equation of the line. In other words we can rephrase this from "is (r,s) on line y=3x+2?" to "Is s=3r+2?"

This Q tests your understanding that the solution of a factored equation that is set to 0 is whatever values will make each factor 0. For instance, statemetn (1) tells us that (3r+2-s)(4r+9-s) = 0. This means that
a. 3r+2-s = 0 --> s=3r+2, or
b. 4r+9-s=0 --> s=4r+9

Since we don't know which is correct, we cannot answer the rephrase. Statement (2) will work the same way. Only when you merge the statements can you definitively know that s=3r+2. The correct answer is C

You can see a video of this solution for a step by step demo; this is QID 1088

-Patrick
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