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In the xy-plane, region R consists of all the points (x,y)

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In the xy-plane, region R consists of all the points (x,y) [#permalink] New post 23 Apr 2010, 03:05
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OG #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

[Reveal] Spoiler:
OA: E
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Re: coord geometry question [#permalink] New post 23 Apr 2010, 16:05
thanatoz wrote:
OG #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

[Reveal] Spoiler:
OA: E


Statement 1:
3r + 2s = 6, r and s can have any real value...!!, Not Sufficient.

Statement 2:
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..
Re: coord geometry question   [#permalink] 23 Apr 2010, 16:05
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In the xy-plane, region R consists of all the points (x,y)

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