In the xy plane, region R consists of all the points (x,y) such that 2x+3y<=6. Is the point (r,s) in the region R?
1. 3r+2s=6
2. r<=3 and s<=2
1. 3r+2s=6
2. r<=3 and s<=2
1. 3r + 2s = 6 has number of possible solutions.
Take r = 1 and s = 1.5. In this case, 2r + 3s = 2 + 4.5 = 6.5, so 2r + 3s is not smaller than or equal to 6.
But if you take r = 2 and s = 0, then you get that 2r + 3s = 4, which is smaller than 6.
This is why 1 is not sufficient.
2. Again, you don't have enough info.
Take r = 1 and s = 1.5 and again, 2r + 3s = 6.5 > 6.
But take r = s = 1 and you get that 2r + 3s = 5 < 6.
This is why 2 is insufficient as well.
Taken together, the two stmts are of no use. The examples given in 1 satisfy stmt 2 as well, so they're enough to prove that E is the answer.
