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X Y Plane

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X Y Plane

by varundaga05 » Wed May 26, 2010 3:38 pm
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 provide a diagram or a simple solution to the problem.
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by varundaga05 » Wed May 26, 2010 3:44 pm
Can we take negative values when it is mentioned r <= 3 and s <=2
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by Rahul@gurome » Wed May 26, 2010 5:22 pm
(1) 3r + 2s = 6 may or may not lie in region R. So, (1) is NOT SUFFICIENT to answer the question.

(2) If we take r = 3 and s = 2, then the point (3, 2) does not lie in region R.
r ≤ 3 and s ≤ 2 implies we can also take negative values for r and s. If r = -2, s = -3, then (-2, -3) lies in region R.
We don't get a unique answer, so (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), if r = 2, s = 0 then (2, 0) lies in region R. But if r = 2/3 and s = 2 then (2/3, 2) lies above the line 2x + 3y = 6, which means (2/3, 2) does not lie in region R. Combining also doesn't give a unique answer.

The correct answer is (E).

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