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Points on an xy plane

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by binaras » Sat Mar 21, 2015 10:53 am
Hi

Need assistance in solving the following DS question

In the xy plane does the line y = 3x + 2 contain the point (r,s)?

1) (3r + 2 - s)(4r + 9 - s)


1) (4r - 6 - s)(3r + 2 - s)

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Mar 21, 2015 10:57 am

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
Target question: Does the line with equation y = 3x + 2 contain the point (r,s)

If (r,s) is on the line defined by the equation y = 3x + 2, then (r,s) must SATISFY the equation y = 3x + 2. In other words, it must be true that s = 3r + 2
For example: We know that the point (5, 17) is on the line y = 3x + 2, because when we plug x = 5 and y = 17 into the equation, we get 17 = 3(5) + 2 and the equation HOLDS TRUE.

So, we can REPHRASE the target question as "Does s = 3r + 2?"

Statement 1: (3r+2-s)(4r+9-s) = 0
From this, we know that EITHER (3r+2-s) = 0 OR (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our REPHRASED target question is no
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our REPHRASED target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since (3r+2-s) is the only expression common to BOTH equations, it MUST be true that 3r+2-s = 0, in which case s MUST equal 3r+2
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C


Cheers,
Brent

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Brent Hanneson - Creator of GMATPrepNow.com
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by binaras » Sat Mar 21, 2015 11:09 am
Thanks for the quick response. Appreciate it.

Binara
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by prada » Wed May 11, 2016 3:20 pm
Brent@GMATPrepNow 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
Target question: Does the line with equation y = 3x + 2 contain the point (r,s)

If (r,s) is on the line defined by the equation y = 3x + 2, then (r,s) must SATISFY the equation y = 3x + 2. In other words, it must be true that s = 3r + 2
For example: We know that the point (5, 17) is on the line y = 3x + 2, because when we plug x = 5 and y = 17 into the equation, we get 17 = 3(5) + 2 and the equation HOLDS TRUE.

So, we can REPHRASE the target question as "Does s = 3r + 2?"

Statement 1: (3r+2-s)(4r+9-s) = 0
From this, we know that EITHER (3r+2-s) = 0 OR (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our REPHRASED target question is no
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our REPHRASED target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since (3r+2-s) is the only expression common to BOTH equations, it MUST be true that 3r+2-s = 0, in which case s MUST equal 3r+2
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C


Cheers,
Brent

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Hi Rich,

On the part below how did you deduce the variables to be in y=mx+b? In other words how did you convert 3r+2-s and decide that
the S plays the role of y, 3R is Mx and 2 is b? They just look live numbers and variables. Thx



If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our REPHRASED target question is no
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