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In the xy-plane, does the line with the equation y = 2x - 4 contain

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In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink]

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New post 20 Jun 2011, 05:50
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-xy-pl ... 40975.html
[Reveal] Spoiler: OA

Last edited by dreambeliever on 20 Jun 2011, 06:07, edited 1 time in total.

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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink]

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New post 20 Jun 2011, 05:59
The answer is C, because there is a common term "(2a - b - 4)" to determine the answer in both (1) and (2), else (1) and (2) on their own give two equations for a and b, while we need a single one in the form 2a - b - 4 = 0 . Can you however clarify if there is a sign missing in this "(4a + 3b 1)" in (2) ?
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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink]

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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink]

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New post 20 Jun 2011, 06:09
subhashghosh wrote:
The answer is C, because there is a common term "(2a - b - 4)" to determine the answer in both (1) and (2), else (1) and (2) on their own give two equations for a and b, while we need a single one in the form 2a - b - 4 = 0 . Can you however clarify if there is a sign missing in this "(4a + 3b 1)" in (2) ?



corrected the missing sign.

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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink]

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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: http://gmatclub.com/forum/in-the-xy-pla ... 00399.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-xy-pl ... 40975.html
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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain   [#permalink] 03 Dec 2017, 23:18
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