g.shankaran wrote: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
IMOc
Solution:
If the line y = 3x +2 has to contain the point (r,s), s = 3r + 2.
First consider (1) alone.
This means that either 3r+2-s = 0 or 4r+9-s = 0.
Since nothing definite can be said, (1) alone is not sufficient.
We next consider (2) alone.
This means that either 3r + 2 - s = 0 or 4r-6-s = 0.
Again, nothing definite can be said.
So, (2) alone is not sufficient.
We next combine both the statements together and check.
On combining, we have that s = 3r + 2.
So, both statements together are sufficient to answer the question.
The correct answer is (C).
