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

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

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10 Apr 2005, 18:10
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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
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10 Apr 2005, 18:15
lot of controversy on this one ....I guess OA is "E"...but some of think it shud be B. Let's see if I can find that thread for u.
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10 Apr 2005, 18:17
banerjeea_98 wrote:
lot of controversy on this one ....I guess OA is "E"...but some of think it shud be B. Let's see if I can find that thread for u.

yes i remember this question
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10 Apr 2005, 23:40
I think I vaguely remember the controversy, but pending Baner's posting of links, I am going to post something for you to critique.

The region R "usually" should be a closed region, but that's not necessary. A region represents a set of points, and in this case, for example, its a straight line.

Now (1) doesnt tell us about the point (r,s). It gives a relationship between r, s and that is a line. So all points lying on that line could be the points r,s. The current case would be easy, since the equation of the line defining (r,s) doesn't coincide with the region defined. So they would intersect at one point, and unless you know the actual values of r,s you cannot tell if the point rs would lie in the region ( = on the line).

Therefore (1) is insufficent.

(2) Clearly defines the point, which makes it easy to figure out if the point r,s lies on the line (in the region) or not. Thus sufficient.

Hence B.
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VP
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11 Apr 2005, 18:21
No, OA is E.

I'm curious about 2nd condition.

Any more idea?
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11 Apr 2005, 18:39
For me it's B but this question has already been posted and discussed many times. People have different opinions so I don't know what to think : 50%B and 50%E...
11 Apr 2005, 18:39
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# In the xy-plane, region R consists of all the points (x, y)

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