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Difficulty:
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Question Stats:
33% (01:59) correct
67%
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wrong
based on 433
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In the xy-plane, does the line with the equation y = 2x - 4 contain the point (a,b)?
(1) (2a - b - 4)(a + 5b + 2) = 0
(2) (4a + 3b - 1)(2a - b - 4) = 0
(1) (2a - b - 4)(a + 5b + 2) = 0
(2) (4a + 3b - 1)(2a - b - 4) = 0
19 Oct 2012, 12:40
Kudos
Bookmarks
Skientist
In the xy-plane, does the line with the equation y=2x-4 contain the point (a,b)?
(1) (2a-b-4)(a+5b+2)=0
(2) (4a+3b-1)(2a-b-4)=0
(1) (2a-b-4)(a+5b+2)=0
(2) (4a+3b-1)(2a-b-4)=0
In the xy-plane, does the line with the equation y=2x-4 contain the point (a,b)?
Line with equation \(y=2x-4\) contains the point \((a,b)\) means that when substituting \(a\) ans \(b\) in line equation: \(b=2a-4\) (or \(2a-b-4=0\)) holds true.
So, basically we are asked to determine whether \(2a-b-4=0\) is true.
(1) (2a-b-4)(a+5b+2)=0 --> either \(2a-b-4=0\) OR \(a+5b+2=0\) OR both. Not sufficient.
(2) (4a+3b-1)(2a-b-4)=0 --> either \(2a-b-4=0\) OR \(4a+3b-1=0\) OR both. Not sufficient.
(1)+(2) Now, since \(a+5b+2=0\) and \(4a+3b-1=0\) can simultaneously be true (for a=11/17 and b=-9/17), then we have that EITHER both \(a+5b+2=0\) and \(4a+3b-1=0\) are true OR \(2a-b-4=0\) is true. Not sufficient.
Answer: E (C is not correct).
Similar question to practice from GMAT Prep: in-the-xy-plane-does-the-line-with-equation-y-3x-100399.html
Hope it helps.
General Discussion
21 Oct 2012, 02:48
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Bookmarks
Bunuel
Skientist
In the xy-plane, does the line with the equation y=2x-4 contain the point (a,b)?
(1) (2a-b-4)(a+5b+2)=0
(2) (4a+3b-1)(2a-b-4)=0
(1) (2a-b-4)(a+5b+2)=0
(2) (4a+3b-1)(2a-b-4)=0
In the xy-plane, does the line with the equation y=2x-4 contain the point (a,b)?
Line with equation \(y=2x-4\) contains the point \((a,b)\) means that when substituting \(a\) ans \(b\) in line equation: \(b=2a-4\) (or \(2a-b-4=0\)) holds true.
So, basically we are asked to determine whether \(2a-b-4=0\) is true.
(1) (2a-b-4)(a+5b+2)=0 --> either \(2a-b-4=0\) OR \(a+5b+2=0\) OR both. Not sufficient.
(2) (4a+3b-1)(2a-b-4)=0 --> either \(2a-b-4=0\) OR \(4a+3b-1=0\) OR both. Not sufficient.
(1)+(2) Now, since \(a+5b+2=0\) and \(4a+3b-1=0\) can simultaneously be true (for a=11/17 and b=-9/17), then we have that EITHER both \(a+5b+2=0\) and \(4a+3b-1=0\) are true OR \(2a-b-4=0\) is true. Not sufficient.
Answer: E (C is not correct).
Similar question to practice from GMAT Prep: in-the-xy-plane-does-the-line-with-equation-y-3x-100399.html
Hope it helps.
Hello Bunuel,
Can you plz explain the highlighed part once again ?
.. cheers 
