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

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Senior Manager
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In the x-y plane, does the line with equation y = 3x + 2 [#permalink]  22 Apr 2007, 08:42
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In the x-y 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
Director
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Re: DS-Question [#permalink]  22 Apr 2007, 10:14
javed wrote:
In the x-y 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

I am looking for a simple and easy way to with this question.
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Re: DS-Question [#permalink]  22 Apr 2007, 10:41
javed wrote:
In the x-y 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,s) lies on y = 3x + 2 then s = 3r + 2

From (1) we have s = 3r+2 and s=4r + 9 so INSUFF
From (2) we have s = 4r + 6 and s = 3r + 2 so INSUFF

From (1) and (2) s = 3r + 2 hence SUFF

SVP
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Director
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Guys, please explain how you solve these equations.

Quote:
(3r + 2 - s)(4r +9 - s) = 0
(4r - 6 - s)(3r + 2 - s) = 0
VP
Joined: 08 Jun 2005
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nick_sun wrote:
Guys, please explain how you solve these equations.

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

you don't have to solve them:

when you know that (3r + 2 - s)(4r +9 - s) = 0

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

but we can't know which one ! (think on (x-2)(x-3) = 0 , either x = 2 or x

= 3 but you can't say for sure which one)

from statement 2 - we know that (4r - 6 - s)(3r + 2 - s) = 0

either (3r + 2 - s) = 0 or (4r - 6 - s) = 0 (same problem as statement 1)

if both statements are correct & using both statements (choice C) we can

say that 3r + 2 - s = 0

if it was not equal 0 then 4r - 6 - s had to be equal to 4r + 9 - s

but we know its not equal !!! (look at -6,9)

hence the the answer is (C)
Senior Manager
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Fig wrote:

y = 3x+2
<3x> 3r+2-s = 0 ? (A)

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

implies that
o 3r+2-s = 0 exactly (A)
or
o 4r+9-s = 0 : 1 point is shared with (A)

INSUFF

Start 1:
(4r-6-s)(3r+2-s) = 0

implies that
o 4r-6-s = 0 : 1 point is shared with (A)
or
o 3r+2-s = 0 exactly (A)

INSUFF

Both (1) & (2)

We have this system of equations :

o 4r+9-s = 0 or 3r+2-s = 0 (I)
AND
o 4r-6-s = 0 or 3r+2-s = 0 (II)

The "and" operand forces to look for an equation in (I) and (II) that guarantes both to be equal to 0. Hence, we have to choose 3r+2-s = 0.

SUFF.

Javed.

Cheers!
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