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In the xy plane, does the line with equation y=3x+2 contain

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In the xy plane, does the line with equation y=3x+2 contain [#permalink] New post 26 Apr 2006, 01:23
In the xy plane, does the line with equation y=3x+2 contain the point (r,s)?

1) (3r+2-s) (4r+9-s)=0
2) (4r-6-s) (3r+2-s)=0
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 [#permalink] New post 26 Apr 2006, 01:44
D...


From the first equation we get

s=3r+2 (this satisfies the GIVEN equation y=3x+r for the values (r,s))
OR
s=4r+9

From seconds equation, we get
s=4r+6
OR
s=3r+2 (this again satisfies)

Combining option 1 AND option 2,
the only soilution that is common is s=3r+2

Hence, it satisfies!
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 [#permalink] New post 29 Apr 2006, 18:33
sm176811 wrote:
D...


From the first equation we get

s=3r+2 (this satisfies the GIVEN equation y=3x+r for the values (r,s))
OR
s=4r+9

From seconds equation, we get
s=4r+6
OR
s=3r+2 (this again satisfies)

Combining option 1 AND option 2,
the only soilution that is common is s=3r+2

Hence, it satisfies!


thanks for the explaination.
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 [#permalink] New post 08 May 2006, 21:43
OA is C... what gives?
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 [#permalink] New post 08 May 2006, 23:06
why do you say:

{Combining option 1 AND option 2,
the only soilution that is common is s=3r+2

Hence, it satisfies!

If we need to combine them to eliminate the OR's, then the correct answer should be C.
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 [#permalink] New post 08 May 2006, 23:12
[quote="stevenzeng"]OA is C... what gives?[/quote]

see my other post. It's C because you need to combine the information to eliminate the OR. The stmts by themselves do not say definitely that the line contains the points.

There's a key to DS problems: Remember that just because you can't say Yes, doesn't mean you can't say NO. I may not be able to say yes to "does x > 0", for example, but one of the stmts may give me enough information to say it definitely is NOT > 0. That's Sufficient.
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 [#permalink] New post 09 May 2006, 10:27
sm176811 wrote:
D...


From the first equation we get

s=3r+2 (this satisfies the GIVEN equation y=3x+r for the values (r,s))
OR
s=4r+9

From seconds equation, we get
s=4r+6
OR
s=3r+2 (this again satisfies)

Combining option 1 AND option 2,
the only soilution that is common is s=3r+2

Hence, it satisfies!


If you combine them then automatically the answer choice is C
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 [#permalink] New post 09 May 2006, 11:25
Would somebody mind explaining how the answer choices fit into what the question is asking? I really don't understand this one...

The way I see it, wouldn't either answer choice be sufficient? Why the need to combine it?
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 [#permalink] New post 10 May 2006, 02:48
stevenzeng wrote:
Would somebody mind explaining how the answer choices fit into what the question is asking? I really don't understand this one...

The way I see it, wouldn't either answer choice be sufficient? Why the need to combine it?



1) (3r+2-s) (4r+9-s)=0

S can have 2 values -
s = 3r + 2 or s = 4r + 9

If s=3r + 2, it satisfies the eq, but for s = 4r + 9, it does not.

Hence insufficient

2) (4r-6-s) (3r+2-s)=0

Here s can have 2 values.
s=4r-6 or s=3r+2

If s=3r + 2, it satisfies the eq, but if s=4r-6, it does not.

Hence insuff

Taking these two together, the only common value of s = 3r+2. This satisfies the eq. Hence sufficient.
Hence C.

Hope it is clear now.
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 [#permalink] New post 11 May 2006, 09:38
However,

Anything multiplied by (3r+2-s) is ZERO, right! Doesn't it mean each of them is sufficient on its own?
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 [#permalink] New post 11 May 2006, 20:06
techno123 wrote:
However,

Anything multiplied by (3r+2-s) is ZERO, right! Doesn't it mean each of them is sufficient on its own?


Yes, my thoughts exactly too. Is there different way we can look at and understasnd this problem?

Thanks..
  [#permalink] 11 May 2006, 20:06
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