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

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Manager
Joined: 19 Aug 2006
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In the xy-plane, region R consists of all the points (x, y) [#permalink]  20 Dec 2006, 06:05
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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
Senior Manager
Joined: 19 Jul 2006
Posts: 361
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Kudos [?]: 3 [0], given: 0

B

(1) 3r + 2s = 6 ...insufficient

(2) if we know the value of r,s ..we can determine if its lie on the line 2x + 3y = 6
Manager
Joined: 19 Aug 2006
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Kudos [?]: 12 [0], given: 0

AK wrote:
B

(1) 3r + 2s = 6 ...insufficient

(2) if we know the value of r,s ..we can determine if its lie on the line 2x + 3y = 6

But here if we draw the line on graph for 2x +3y =6 then we dont know which side area lies. so we cant predict whether r,s is in area or out of the area.
Senior Manager
Joined: 08 Jun 2006
Posts: 342
Location: Washington DC
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B for me too...

From 1) Intersecting line ... In area and out of area ..both possible
From 2) just one point ..clearly not on the given line..

I am not clear with one point...why the question talks about a region but provides a equation of a st line..I am not getting how the region is formed.
Can someone throw some light..?
Senior Manager
Joined: 04 Nov 2006
Posts: 267
Location: California
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Kudos [?]: 61 [0], given: 0

B.. too..

Line is a subset of region.. It is like saying rhombus is a subset of quadrangles.. on the same logic, line is a region which has 0 area..
Manager
Joined: 19 Aug 2006
Posts: 222
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Kudos [?]: 12 [0], given: 0

But OA is E.
Senior Manager
Joined: 04 Nov 2006
Posts: 267
Location: California
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Kudos [?]: 61 [0], given: 0

How E?

If you plug in, r and s, it does not satisfy the eqn.. hence r,s is not in the region.

OA is wrong..

A is clearly can't say.. this line will intersect the original line.. so A is not answer...
Senior Manager
Joined: 24 Oct 2006
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