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

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a.k.bhageria
 Post subject: In the xy-plane does the line with equation y = 3x + 2 ...
 Post Posted: Sat Jul 03, 2010 8:35 am 
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Students


Posts: 11
Location: Mumbai
Hi, I encountered this problem in my GMATPrep test-

Data sufficiency:
In the xy-plane does the line with equation y = 3x + 2 contain (r,s)
1. (3r + 2 - s)(4r + 9 - s) = 0
2. (4r - 6 - s)(3r + 2 - s) = 0

I answered - Both individually sufficient. The way i approached it was- replaced (r,s) in the required line eq. i.e. s = 3r + 2. If this equation is proved from the options then they're sufficient.
Now instead of solving each equation (which seemed like a lengthy process), I substituted s=3r+2 in each of the 2 options. Because I got 0 = 0, I concluded that this value of s is a solution for each of the two equations. Hence chose the answer.

Can you please tell me why this approach is wrong and how to solve it alternatively?

Thanks
Ankur
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adiagr
 Post subject: Re: In the xy-plane does the line with equation y = 3x + 2 ...
 Post Posted: Sat Jul 03, 2010 9:57 am 
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Students


Posts: 89
a.k.bhageria wrote:
Hi, I encountered this problem in my GMATPrep test-

Data sufficiency:
In the xy-plane does the line with equation y = 3x + 2 contain (r,s)
1. (3r + 2 - s)(4r + 9 - s) = 0
2. (4r - 6 - s)(3r + 2 - s) = 0

I answered - Both individually sufficient. The way i approached it was- replaced (r,s) in the required line eq. i.e. s = 3r + 2. If this equation is proved from the options then they're sufficient.
Now instead of solving each equation (which seemed like a lengthy process), I substituted s=3r+2 in each of the 2 options. Because I got 0 = 0, I concluded that this value of s is a solution for each of the two equations. Hence chose the answer.

Can you please tell me why this approach is wrong and how to solve it alternatively?

Thanks
Ankur


Hi,

(r,s) will lie on the line with equation y = 3x + 2, if in place of x and y respectively we put the coordinates of the point and the line equation is satisfied.

So , (r,s) will lie on y = 3x +2, if s=3r+2 or in other words:

3r-s+2 = 0.



From St. 1:

(3r + 2 - s)(4r + 9 - s) = 0
i.e.

either

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


Say (3r + 2 - s) = 0 -->St. 1 satisfied and (r, s) lies on given line.


Now say, (3r + 2 - s) not equal to zero, but
(4r + 9 - s) = 0

Then St. 1 satisfied but (r, s) does not lie on given line.

So St. 1 is not sufficient.

Exactly same logic for St. 2.

St. 2 not sufficient.

Combining both statements.


case 1: (3r + 2 - s) is equal to zero

case 2: (3r + 2 - s) is not equal to zero

let's discuss case (2):

This means that

(4r + 9 - s) = 0 and also (4r - 6 - s) = 0

which is absurd. (4r-s = -9 as well as 6--> not possible)

so only case 1 holds i.e.

(3r + 2 - s) is equal to zero


(C) is the answer.
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a.k.bhageria
 Post subject: Re: In the xy-plane does the line with equation y = 3x + 2 ...
 Post Posted: Sat Jul 03, 2010 12:22 pm 
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Students


Posts: 11
Location: Mumbai
Oh right.. ofcourse.. never ignore the other bracket.. thanks for the solution. Much appreciated.
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mschwrtz
 Post subject: Re: In the xy-plane does the line with equation y = 3x + 2 ...
 Post Posted: Mon Jul 12, 2010 11:46 pm 
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ManhattanGMAT Staff


Posts: 506
ty again adiagr
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