Data Sufficiency

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


from the equation y = 3x + 2, we get to know that SLOPE = 3. so point (r,s) should also have the same slope.

By solving statement 1, we get
s = 3r + 2 and s = 4r + 9
so, the slope = 3 or 4

By solving statement 2, we get
s = 4r - 6 and s = 3r + 2
so, the slope = 4 or 3

Now considering both statements, we get SLOPE = 3 or 4. so i selected "E". But the OA is "C"

Please help to clarify the same.

Thanks & Regards
Nikunj

The question asks if y = 3x + 2 contain the point (r,s)
=> is S=3r+2??

From option 1 we get S=3r+2 or S=4r+9
So option 1 is insff

From option 2 we get S=4r-6 or S=3r+2
So option 2 is insuff

Considering both we can conclude that S=3r+2
Hence the answer is C.....Hope this clarifies your doubt

Thanks jahnaviyeruva. Now I got it.

IMO C

jahnaviyeruva wrote:
Considering both we can conclude that S=3r+2
Hence the answer is C.....Hope this clarifies your doubt

even if we don't now what the values of S and R is the answer C because we hypothetically could use algebra to solve for them (not that we would)?

Or is there another reason why the two taken together are suff?