Problem Solving

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

Here is my Solution:
This is a yes/no DS problem

For point (r,s) to lie on line with equation y = 3x + 2, it must satisfy this equation i.e., we should be able to get s = 3r + 2

I) (3r + 2 - s) = 0 or (4r + 9 - s) = 0 i.e.,
s = 3r + 2 or ===> Yes
s = 4r + 9 ===> No
Insufficient

II) (4r - 6 - s) = 0 or (3r + 2 - s) = 0
s = 4r - 6 ===> No
s = 3r + 2 ===> Yes
Insufficient


I & II together: This is where i am confused.

If i consider that the common from both statements, then i get answer as C (Both together are sufficient)
In that case what happens to the other two values/equations which are not common in I & II.

I would really appreciate any help to clarify my doubt.

Thanks,
Harmeet.

Hi Harmeet,

When both statements are considered together, there can only be 2 conditions:
1) (r,s) is on the line or
2) (r,s) is not on the line.

First let us assume that (r,s) is on the line.
In this case we know that s=3r+2

So we have to take s=3r+2 from both premise1 and premise2
And we are saying that (r,s) is on the line.

Now let us say, (r,s) is not on the line.
So we need to take the other two statements form premise1 and premise2
So, we get s=4r+9 and s=4r-6

This is not possible because it means to say that 9=-6

so (r,s) is not (not on th line)

Hence (r,s) should be on the line.
So Answer should be C. BTW what is OA?

Please let me know if there is any mistake in my assumptions..

Your thinking right up until the point of combining is great!

Can both of (4r - 6 - s) and (4r + 9 - s) simultaneously equal 0?...

This is not possible because it means to say that 9=-6

Perfect....choose C!

@harmeet: please post DS questions in the DS (and not the PS) forum!

Good Question..I would have definitely gone confused on the test day..

Now I know how to deal with it

Thank you every one.
Next time i will remember to put DS Q's in DS section. Sorry about that !!