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

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Intern
Joined: 07 Oct 2004
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In the xy-plane, region R consists of all the points (x, y) [#permalink]  09 Oct 2004, 09:09
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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

what exactly is the definition of region?
Manager
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[#permalink]  09 Oct 2004, 12:22
D

If we substitute value for x and y in 2x+3y and get 6 as the result then those values belong to region R.
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[#permalink]  09 Oct 2004, 12:50
Then why D and not B?

If you take r = 0 and s = 3 then it fullfills statement 1 but it does not apply to Region R.
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[#permalink]  09 Oct 2004, 13:23
The region R defined by 2x+3y=6 is a straight line

for statement 1 we have 3r+2s=6 which gives that (r,s) are on a straight line different than R. so (r,s) does not necessary belong. but we have to make sure that it intersects it. (to prove that it belongs and doesn't belong)
as you can see from the 2 straight lines we have an intersection (6/5,6/5). so statement one is insufficient

for statement 2 we have the point (3,2) plugging it in the the straight line
2x+3y=6 we can know if it belongs or not. so statement 2 is sufficient

Answer is indeed B
[#permalink] 09 Oct 2004, 13:23
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# In the xy-plane, region R consists of all the points (x, y)

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