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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 07 Dec 2004, 08:04
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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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 [#permalink] New post 07 Dec 2004, 08:39
B

Stem: 2x + 3y = 6

s[1]: 3r+2s = 6
There are several numbers (r,s) that will fit the equation. So, without knowing the exact value of (r,s) we cannot say if it fits the equation in the stem.
Insufficient

S[2]: r=3, s=2
=> 2r+3s = 6+6 =12, so they do not fit the region R.
Sufficient
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Re: DS - Co Geo [#permalink] New post 07 Dec 2004, 10:04
crackgmat04 wrote:
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


Agree with B. The second one is obvious. It's definately going to work one way or the other.

The first one says that 3r + 2s = 6. That means there are an infinate number of pairs (r,s). Only one of them will fit the equation 2x+3y=6, so it's not enough information.

But I have a problem with this question. If number 2 is right (and since it's DS, it's a statement of fact) then r = 3 and s = 2. That doesn't jive with number one, which says that 3r + 2s = 6. Plugging in the givens in number 2, 3r + 2s would equal 9 + 4 = 13.

NEVER FORGET THIS: the statements on real GMAT data sufficiency questions will never be talking about a different situation. If those are the points in 2, they will be the points in 1, whether we can logically arrive at them or not. This is critical for seeing the GMAT in the proper light. Never take the two statements in a vacuum from one another, even if the answer is A,B or D. We can always use the information we learn from one to evaluate the other, even if it's not C.
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 [#permalink] New post 07 Dec 2004, 11:09
I think B is the answer but it doesn't fit in the region given by equation 3x+2y = 6. If you put in the values of r=3 and s=2, it is 12=6, so it doesn't fit in the region, although it does answer the question.
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 [#permalink] New post 07 Dec 2004, 11:21
I am not sure about this one.

lets look a statment 1:
it can be a line that intersect with the line in the questions:
we can look at r,s as x,y or r,s y,x

if r,s is y,x so it is the same like the question so it is true
if r,s is y,x so (6/5,6/5) is point that the two line intersect.
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Re: DS - Co Geo [#permalink] New post 12 Dec 2004, 12:47
ian7777 wrote:
crackgmat04 wrote:
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


Agree with B. The second one is obvious. It's definately going to work one way or the other.

The first one says that 3r + 2s = 6. That means there are an infinate number of pairs (r,s). Only one of them will fit the equation 2x+3y=6, so it's not enough information.

But I have a problem with this question. If number 2 is right (and since it's DS, it's a statement of fact) then r = 3 and s = 2. That doesn't jive with number one, which says that 3r + 2s = 6. Plugging in the givens in number 2, 3r + 2s would equal 9 + 4 = 13.

NEVER FORGET THIS: the statements on real GMAT data sufficiency questions will never be talking about a different situation. If those are the points in 2, they will be the points in 1, whether we can logically arrive at them or not. This is critical for seeing the GMAT in the proper light. Never take the two statements in a vacuum from one another, even if the answer is A,B or D. We can always use the information we learn from one to evaluate the other, even if it's not C.



what ian has said is indeed valuable info to remember....i wud say whoever framed this question did not do a good job ...
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 [#permalink] New post 12 Dec 2004, 13:34
Agree with people that statements 1 and 2 don't jive together. Let me solve this anyway

1) 3r + 2s =6

All possible solutions of this equation will not fit in 2x + 3y = 6. But some might like (6/5, 6/5)
So this is out.

2) Simple, it does not fit in 2x + 3y = 6.
OK

Together the 1) and 2) don't fit together at all as they contradict each other.
:idea:
If an answer has to be given, it is B.
  [#permalink] 12 Dec 2004, 13:34
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