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

[a.k.bhageria]

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

[adiagr]

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.

[a.k.bhageria]

Oh right.. ofcourse.. never ignore the other bracket.. thanks for the solution. Much appreciated.

[mschwrtz]

ty again adiagr

[sachin.w]

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

substitute (r,s) in y = 3x + 2

=>
s=3r+2

This is substituted in (1) and (2)

will make LHS=RHS in both cases. So I chose D.

I am not understanding why the above approach is wrong.

[RonPurewal]

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

substitute (r,s) in y = 3x + 2

=>
s=3r+2

This is substituted in (1) and (2)

will make LHS=RHS in both cases. So I chose D.

I am not understanding why the above approach is wrong.

whoa, looks like you have to go back to the very beginning and strengthen your foundation in data sufficiency. you're working the whole problem backward.

in a data sufficiency problem, you should assume that each of the numbered statements, in turn, is true, and then check the answer to the QUESTION.
instead, you are assuming that the statement in the QUESTION is true, and then testing the STATEMENTS. that's not how this problem format works.

here's a simpler example:
Is x > 3?
(1) x > 1
(2) x > 5
the correct answer to this is (b). if you know x > 5, then the answer to the question is "yes". (the first statement isn't sufficient, since knowing x > 1 doesn't guarantee whether x is greater than 3.)
if you take the approach you're taking above, then you'll mistakenly conclude that the answer to this question is (a).
i.e., if you take your approach above, then you'll assume x > 3 and then ask whether x > 1, and you'll erroneously conclude that statement (1) is a "yes" answer.

[sachin.w]

Thanks a lot, Ron. Example makes the confusion get washed away!

[tim]

:)