Data Sufficiency

What is the fastest way to approach the following question?

In the xy plane, Region R consists of all points (x,y) such that 2x+3y<or=6. Is the point (r,s) in Region R?

(1) 3r+2s=6
(2) r<or=3 and s<or=2



Answer is......E.

Thanks, John

let me take a crack at this.

stmt 1: 3r +2s = 6.
This is insufficient coz only one point (x,y) (possibly few more points coz of the <= symbol in the Q ) will lie on the straight line. This point can be found out by replacing r,s with x,y respectively and solving the simultaneous equations. 3x +2y =6 and 2x +3y <= 6.

So insufficient.


Stmt2: r <=3 and s <=2

r and s can be any value. And their combination need not satisfy the eqn for Region R.
Hence insufficient.

Combining them does not yield a single solution. coz some points can be in R and some may not be.
So E

HT Helps

2x+3y<=6 is the line that intercepts y axis in (0,2) point and X axis at (3,0) point. All points below this line denotes the region of (x,y)

STMT 1 clearly doesn't satisfy this condition.

but as per my graph, STMT #2 satisfies this condition

Take any value of r,s where r<=3 and s <=2 and 2r+3s <=6.

Can someone explain why not (B) ?

Bidisha800 wrote:2x+3y<=6 is the line that intercepts y axis in (0,2) point and X axis at (3,0) point. All points below this line denotes the region of (x,y)

STMT 1 clearly doesn't satisfy this condition.

but as per my graph, STMT #2 satisfies this condition

Take any value of r,s where r<=3 and s <=2 and 2r+3s <=6.

Can someone explain why not (B) ?

from the graph we can see that x have to < =3 and y < = 2
but there can be combinations like

( 3, 1 ) which would not satisfy the orginal equation...

Its great to see some GMAT focus question here. Can you share some more of them please? Or if possible all? Please comment. I am awaiting for ur resposnse.

As for as solving goes:

You need to make an XY graph and cover the appropriate region covered by the line, it will give you the clue. You may refer similar Q in OG books too.

Regards,
nagendra