Help - GMAT Prep Ques 2 - See screenshot

[charu_mahajan]

Kindly let me know how to solve this.

[niketdoshi123]

If the lines with equation y=3x+2 contains the point (r,s), then r&s should satisfy the equation of the line.
i.e s=3r+2 (required)

Statement 1
(3r+2-s)(4r+9-s)=0
so either (3r+2-s)=0 or (4r+9-s)=0
from 1st equation we get s=3r+2, which is required.
from 2nd equation we get s=4r+9, which is not required.
Hence the statement is INSUFFICIENT

Statement 2
(4r-6-s)(3r+2-s)=0
We can solve this the same way we did above.
Similarly this statement is also INSUFFICIENT

Combining both the statements
we can equate both the equations

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

By assuming (3r+2-s) to be non zero be can cancel it from both the sides.
Now we are left with

(4r+9-s)=(4r-6-s)
=>9=-6 Not true. This means that our previous assumption was wrong and
(3r+2-s) (must be) =0
Hence SUFFICIENT

So the answer is C

[charu_mahajan]

Thanks a lot!!

[mdavidm_531]

Thanks a lot!!

With this type of questions, I'd be more fitting to know the following algebraic translations:

"OR" means multiplication

"ADD" means addition

Statement (1) presents an "OR" statement that's why it's insufficient.

Statement (2) presents an "OR" statement that's why it's insufficient.

Statement (1) AND (2) presents an "ADD" statement that's why we get the "intersection" of the two statements