[email protected] wrote:121. 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
Please do not share the OG answer..
Approach 1:
Question rephrased: Is 2r+3s≤6?
Try to plug in values that satisfy both statements.
Maximize r in one case and s in the other.
r maximized:
r=3 and s=0 satisfy both statements.
Is 2(3) + 3(0) ≤ 6?
YES.
s maximized:
r=2/3 and s=2 satisfy both statements.
Is 2(2/3) + 3(2) ≤ 6?
NO.
Since in the first case the answer is YES and in the second case the answer is NO, the two statements combined are INSUFFICIENT.
The correct answer is
E.
Approach 2:
Region R comprises all the points on or below y=(-2/3) + 2.
Statement 1: s = (-3/2)r + 3.
The figure above shows that some points on s=(-3/2)r + 3 lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.
Statement 2: r≤3 and s≤2.
Inside the green box are points such that r≤3 and s≤2.
Some of the points inside the green box lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.
Statements 1 and 2 combined:
Inside the green box are points on s=(-3/2)r + 3.
Some of these points lie BELOW y=(-2/3)r + 2, while others lie ABOVE y=(-2/3)r + 2.
INSUFFICIENT.
The correct answer is
E.
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