DS - CG

[rkhicha]

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

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

Thanks.

[Rahul@gurome]

The question becomes is s = 3r + 2?
(1) (3r+2-s)(4r+9-s)=0 implies either 3r+2-s = 0 or 4r+9-s = 0, which is NOT SUFFICIENT.

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

Combining (1) & (2), 3r+2-s = 0 or 3r + 2 = s is true.

[spoiler]The correct answer is (C).[/spoiler]

[Patrick_GMATFix]

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

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

The equation of the line is y=3x+2, where x and y represent the coordinate of any point (x,y) on that line. For point (r,s) to be on the line, it must be the case that s=3r+2.

Rephrase the question as: "Is s=3r+2?"

Statement (1) tells you that
---> 3r+2-s=0 --> s=3r+2 OR
---> 4r+9-s=0 --> s=4r+9.

Because we don't know whether s is 3r+2 or 4r+9, we cannot answer the rephrase. Statement (2) works the same way. You must merge the statements to solve because once the statements are merged the only value of s that agrees with both statements is s=3r+2. [spoiler]C is the answer.
[/spoiler]
You can view a much more detailed explanation and a step-by-step video solution at GMATPrep Question 1088. To practice similar questions in timed drills, set topic='Geometry, Coordinate' and difficulty='600-700' in the Drill Generator

Hope that helped,
-Patrick

PS: This question is also discussed here