In the xy-plane, does the line

[ayushiiitm]

In the xy-plane, does the line in question y=3x+2 contain the point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

My take:

For stem 1
3r-s=2---(1)
4r-s=9---(2)

Solve for r and s, put in equation and find out yes/no

Similarly possible for stem 2

Hence, IMO D

OA [spoiler]:C[/spoiler]

[outreach]

Does s = 3r + 2? or 3r +2 - s = 0?

(1) either 3r + 2 - s = 0 OR that 4r + 9 - s = 0. Insufficient.
(2) either 4r - 6 - s = 0 OR that 3r + 2 - s = 0. Insufficient.
(1&2) The only possibility that would satisfy both statements is that 3r + 2 - s = 0. Sufficient

[Patrick_GMATFix]

Hi Ayushiitm,

The OA is correct. D is not the answer. 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

[ayushiiitm]

yeah got it...Thanks

[Patrick_GMATFix]

No problem mate.