Data Sufficiency

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

OA C

Can anyone explain in detail?

selango wrote: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

OA C

Can anyone explain in detail?

If (r,s) lie on the line then it has to satisfy the equation y=3x+2 contain the point (r,s)

So it becomes like: s= 3r+2

Combining st 1 & st2 :

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

(3r+2-s) {(4r+9-s) +(4r-6-s) }=0

(3r+2-s) {15} =0

--->(3r+2-s) =0

---> 3r+2 =s

pick C

When asked if a point is on a certain line, test whether or not it satisfies the equation of the line.

The question can actually be summarized to : Is s = 3r + 2

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

=> 3r + 2 - s = 0 OR 4r + 9 - s =0
=> s = 3r + 2 (on the line)OR s = 4r + 9 (not on the line)

INSUFFICIENT

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

=>4r - 6 - s = 0 OR 3r + 2 - s = 0
=> s = 4r + 6(on the line)Or s = 3r + 2(not on the line)

INSUFFICIENT

Both 1 and 2.

The common solution is only s = 3r + 2 (on the line)... SUFFICIENT

Pick C.