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In the Xy plane, does the line with equation y=3x+2 contain
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13 Dec 2009, 04:25
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In the Xy plane, does the line with equation y=3x+2 contain the point (r,s) ? (1) (3r+2s)(4r+9s)=0 (2) (4r6s)(3r+2s)=0 OPEN DISCUSSION OF THIS QUESTION IS HERE: inthexyplanedoesthelinewithequationy3x100399.html
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Re: Math (DS)
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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



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Re: Math (DS)
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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+2s)(4r+9s)=0 2.(4r6s)(3r+2s)=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+2s 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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Re: Math (DS)
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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+2s)(4r+9s)=0 2.(4r6s)(3r+2s)=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 (4r6s)(ss) = 0 true again, r and s must be on the line ==> sufficient
my answer D
what is OA ?



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Re: Math (DS)
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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+2s)(4r+9s)=0 2.(4r6s)(3r+2s)=0
Equation 1 suggests either (3r+2s)=0 or (4r+9s) = 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+2s)=0 or (4r6s) = 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+9s=0 and 4r6s cannot be true together hence 3r+2s =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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Re: Math (DS)
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11 Jan 2010, 23:38
silasaaa2 wrote: In the Xy plane, does the line with equation y=3x+2 contain the point (r,s) ?
1.(3r+2s)(4r+9s)=0 2.(4r6s)(3r+2s)=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 \(3r+2s=0\)) holds true. So basically we are asked to determine whether \(3r+2s=0\) is true or not. (1) \((3r+2s)(4r+9s)=0\) > either \(3r+2s=0\) OR \(4r+9s=0\) OR both. Not sufficient. (2) \((4r6s)(3r+2s)=0\) > either \(3r+2s=0\) OR \(4r6s=0\) OR both. Not sufficient. (1)+(2) Both \(4r+9s=0\) and \(4r6s=0\) can not be true (simultaneously), hence \(3r+2s=0\) must be true. Sufficient. Answer: C.
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Re: Math (DS)
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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+2s)=0
 the line does not contains (r,s) meaning (4r+9s)=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+2s)=0
 the line does not contains (r,s) meaning (4r6s)=0
When we combine (1) and (2) we know that either  (3r+2s)=0
 (4r+9s)=0=(4r6s)
We can algebraically prove the second answer is impossible \(4r+9s=4r6s\) eliminate the s by adding s to both sides \(4r+9=4r6\) elimated the 4r by subtracting 4r from both sides \(9=6\) < obviously this is not possible So then we know 3r+2s=0 which means s=3r+2 in the (x,y) notation y=3x+2



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Re: straight line equation
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15 Aug 2010, 22:15
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+9s = 0, then (r,s) does not lie on our line. Hence, insufficient. Stmt 2 If (4r  6  s)(3r + 2  s) = 0 then either 4r6s = 0 or 3r+2s = 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+2s has to be zero because; 4rs cannot simultaneously be equal to 9 AND +6. Since, 3r+2s = 0; (r,s) lies on our line. Hence, sufficient. Hope this helps. Thanks.
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Re: Points on a line
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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+9s = 0, then (r,s) does not lie on our line. Hence, insufficient. Stmt 2 If (4r  6  s)(3r + 2  s) = 0 then either 4r6s = 0 or 3r+2s = 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+2s has to be zero because; 4rs cannot simultaneously be equal to 9 AND +6. Since, 3r+2s = 0; (r,s) lies on our line. Hence, sufficient. Hope this helps. Thanks. _________________ Naveenan Ramachandran 4GMAT  Mumbai
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Re: Math (DS)
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23 Nov 2010, 23:08
Bunuel wrote: silasaaa2 wrote: (1)+(2) Both \(4r+9s=0\) and \(4r6s=0\) can not be true (simultaneously), hence \(3r+2s=0\) must be true. Sufficient.
Answer: C.
My answer is c. But i did not think that (1) and (2) need checking not only the posibility of 3r+2s=0 but also another posibility of whether 4r + 9 s = 4e6s = 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
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29 Sep 2018, 03:43
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