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

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Manager
Joined: 26 Nov 2009
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In the Xy plane, does the line with equation y=3x+2 contain  [#permalink]

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13 Dec 2009, 04:25
1
5
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Difficulty:

65% (hard)

Question Stats:

62% (00:37) correct 38% (01:05) wrong based on 103 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-xy-plane-does-the-line-with-equation-y-3x-100399.html
Manager
Joined: 26 Nov 2009
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13 Dec 2009, 05:03
by solving both the algebaric equations i was able to identify that both are required but under the actual test conditions i guessed it has to be either b or e and my luck i chose e
Manager
Joined: 09 May 2009
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14 Dec 2009, 09:41
silasaaa2 wrote:
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

on exam day certainly to solve this is going to kill my time ,
rather seeing bth the statements we come to knw that 3r+2-s is common and hence has to be = zero which is nthng but eqn of the line y=3x+2 passing through r,s
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Manager
Joined: 06 Jan 2010
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11 Jan 2010, 19:26
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

if r and s is point on the line, then s = 3r + 2

statement 1
( s + 2 - s)() = 0
true
r and s must be on the line ==> sufficient

statement 2
(4r-6-s)(s-s) = 0
true
again, r and s must be on the line ==> sufficient

what is OA ?
Intern
Joined: 20 Oct 2009
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11 Jan 2010, 23:36
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

Equation 1 suggests
either (3r+2-s)=0 or (4r+9-s) = 0
Now if stmt 1 is true then the line with equation y=3x+2 contains the point (r,s) but not so for equation 2..Ambiguity

Equation 2
either (3r+2-s)=0 or (4r-6-s) = 0
Now if stmt 1 is true then the line with equation y=3x+2 contains the point (r,s) but not so for equation 2..Ambiguity

Taking equation 1 & 2 together
We know 4r+9-s=0 and 4r-6-s cannot be true together hence 3r+2-s =0 and hence the line with equation y=3x+2 contains the point (r,s) ...Sufficient.

Hence both statements together are sufficient though each individually is not sufficient (OA : C)
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Joined: 02 Sep 2009
Posts: 50042

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11 Jan 2010, 23:38
5
1
silasaaa2 wrote:
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

No need to solve the system of equations.

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ can not be true (simultaneously), hence $$3r+2-s=0$$ must be true. Sufficient.

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30 Jul 2010, 08:16
Please remember the question here. Is (r,s) on the line $$y=3x+2$$ or not on the line

Based on reasoning explained above, if we have only statement (1) there are two possible situations
• either the line contains (r,s) meaning (3r+2-s)=0
• the line does not contains (r,s) meaning (4r+9-s)=0

Because (1) is not sufficient we look at (2) alone

If we have only statement (2) there are two possible situations
• either the line contains (r,s) meaning (3r+2-s)=0
• the line does not contains (r,s) meaning (4r-6-s)=0

When we combine (1) and (2) we know that either
• (3r+2-s)=0
• (4r+9-s)=0=(4r-6-s)

We can algebraically prove the second answer is impossible
$$4r+9-s=4r-6-s$$
eliminate the s by adding s to both sides
$$4r+9=4r-6$$
elimated the 4r by subtracting 4r from both sides
$$9=-6$$ <-------- obviously this is not possible

So then we know 3r+2-s=0
which means s=3r+2
in the (x,y) notation y=3x+2
Intern
Joined: 15 Aug 2010
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Location: Mumbai
Schools: Class of 2008, IIM Ahmedabad

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15 Aug 2010, 22:15
1
Hi,

Stmt 1

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

then either the 3r + 2 - s = 0 or 4r + 9 - s = 0.

If 3r + 2 - s = 0, then (r,s) lies on the line y=3x + 2

However, if 4r+9-s = 0, then (r,s) does not lie on our line.

Hence, insufficient.

Stmt 2

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

then either 4r-6-s = 0 or 3r+2-s = 0

If the former is true (r,s) does not lie on our line. If the latter is true, (r,s) does lie on our line.

Hence, insufficient.

Combine both statements:

(3r + 2 -s)(4r + 9 - s) = 0
(4r - 6 - s)(3r + 2 - s) = 0

3r+2-s has to be zero because; 4r-s cannot simultaneously be equal to -9 AND +6.

Since, 3r+2-s = 0; (r,s) lies on our line. Hence, sufficient.

Hope this helps. Thanks.
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Naveenan Ramachandran
4GMAT - Mumbai

Intern
Joined: 15 Aug 2010
Posts: 22
Location: Mumbai
Schools: Class of 2008, IIM Ahmedabad
Re: Points on a line  [#permalink]

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22 Aug 2010, 21:21
Hi,

Stmt 1

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

then either the 3r + 2 - s = 0 or 4r + 9 - s = 0.

If 3r + 2 - s = 0, then (r,s) lies on the line y=3x + 2

However, if 4r+9-s = 0, then (r,s) does not lie on our line.

Hence, insufficient.

Stmt 2

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

then either 4r-6-s = 0 or 3r+2-s = 0

If the former is true (r,s) does not lie on our line. If the latter is true, (r,s) does lie on our line.

Hence, insufficient.

Combine both statements:

(3r + 2 -s)(4r + 9 - s) = 0
(4r - 6 - s)(3r + 2 - s) = 0

3r+2-s has to be zero because; 4r-s cannot simultaneously be equal to -9 AND +6.

Since, 3r+2-s = 0; (r,s) lies on our line. Hence, sufficient.

Hope this helps. Thanks.

_________________
Naveenan Ramachandran
4GMAT - Mumbai
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Naveenan Ramachandran
4GMAT - Mumbai

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Status: what we want to do, do it as soon as possible
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23 Nov 2010, 23:08
Bunuel wrote:
silasaaa2 wrote:

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ can not be true (simultaneously), hence $$3r+2-s=0$$ must be true. Sufficient.

My answer is c. But i did not think that (1) and (2) need checking not only the posibility of 3r+2-s=0 but also another posibility of whether 4r + 9 -s = 4e-6-s = 0.
Thanx Bunuel, you really made it as far as it should be.
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Re: In the Xy plane, does the line with equation y=3x+2 contain  [#permalink]

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29 Sep 2018, 03:43
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