In the xy-plane, region R consists of all the points (x,y) such that 2x+3y =< 6. Is the point (r,s) in region R?
1) 3r + 2s = 6
2) r =< 3 and s =< 2
3r + 2s = 6, r and s can have any real value...!!, Not Sufficient.
This statement is bit tricky..
We draw the straight line 2x+3y = 6, and then shade the area 2x+3y =< 6,
plug in the value of r=3 and s=2, we will find 2x+3y =12, but 2x+3y should be less than equal to 6.
so r,s lies outside the region marked by 2x+3y =< 6, but if we choose r=0 and s=0, the point r,s lies in the given region. Not sufficient.
Statement 1 and Statement 2:
Together not sufficient..