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

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Intern
Joined: 12 Apr 2009
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In xy-plane, does line with equation y = 3x+2 contain the [#permalink]

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12 May 2009, 17:34
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In xy-plane, does 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

Kudos [?]: 6 [0], given: 2

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1063 [1], given: 5

Location: New York
Re: DS Question 2 [#permalink]

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12 May 2009, 19:58
1
KUDOS
meesawoosa wrote:
In xy-plane, does 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

rewrite the question stem:
Is s=3r+2 ? (i.e 3r-s+2=0?)

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

not sufficient

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

combined
assume that (4r+9-s)=0 then (4r-6-s) definitely <>0 so (3r +2-s) =0 must satisfy.

C is the answer.
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Kudos [?]: 1063 [1], given: 5

Director
Joined: 23 May 2008
Posts: 801

Kudos [?]: 84 [0], given: 0

Re: DS Question 2 [#permalink]

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12 May 2009, 21:47
x2suresh wrote:
meesawoosa wrote:
In xy-plane, does 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

rewrite the question stem:
Is s=3r+2 ? (i.e 3r-s+2=0?)

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

not sufficient

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

combined
assume that (4r+9-s)=0 then (4r-6-s) definitely <>0 so (3r +2-s) =0 must satisfy.
C is the answer.

i found both statements insufficient but couldnt see how the answer could be C

can you elaborate on C? I dont really understand your rationalization

Kudos [?]: 84 [0], given: 0

Manager
Joined: 14 May 2009
Posts: 191

Kudos [?]: 48 [0], given: 1

Schools: Stanford, Harvard, Berkeley, INSEAD
Re: DS Question 2 [#permalink]

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14 May 2009, 13:52
meesawoosa wrote:
In xy-plane, does line with equation y = 3x+2 contain the point (r,s)?

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

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

If (r,s) is on the line y=3x+2, then we can substitute in y=s & x=r into the equation to get,
Question:($$s=3r+2$$)?
Question:($$3r+2-s=0$$)?

(1) $$(3r +2-s)(4r+9-s)=0$$
This implies that either $$3r+2-s=0$$ or $$4r+9-s=0$$, the first equation gives us a YES, the second one a NO. Insufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$
This implies that either $$4r-6-s=0$$ or $$3r+2-s=0$$, the first equation gives us a YES, the second one a NO. Insufficient.

(1&2) Combining the facts above gives us
$$3+2-s=0$$ OR $$4r+9-s=0$$
AND
$$4r-6-s=0$$ OR $$3r+2-s=0$$

This implies that $$3r+2-s=0$$ is true, what we're trying to find.

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Kudos [?]: 48 [0], given: 1

Re: DS Question 2   [#permalink] 14 May 2009, 13:52
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In xy-plane, does line with equation y = 3x+2 contain the

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