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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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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

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Originally posted by Skientist on 19 Oct 2012, 12:13.
Last edited by Bunuel on 04 Dec 2017, 00:18, edited 3 times in total.
Renamed the topic, edited the question and the OA.
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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 19 Oct 2012, 12:40
4
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Skientist wrote:
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


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.
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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 21 Oct 2012, 02:48
Bunuel wrote:
Skientist wrote:
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


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 ?
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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 21 Oct 2012, 05:54
1
154238 wrote:
Bunuel wrote:
Skientist wrote:
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


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 ?


We have two equations,

We are asked whether a = 0.

1) ab = 0

2) ac = 0

From 1, the following situations are possible
a = 0 or
b = 0 or
Both a & b are 0

So a can be 0 or non zero. So insufficient.

From 2, the following situations are possible
a = 0 or
c = 0 or
Both a & c are 0

So a can be 0 or non zero. So insufficient.

1 & 2 together

a can be non zero while b and c could be 0. or
a can be 0 while b and c could be non zero. or
a,b & c all three can be 0.

So it is still not possible to determine whether a is zero or not.

Hence answer is E
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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 21 Oct 2012, 06:18
Got it buddy !!
Kudos for you :-D .. cheers
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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 23 Oct 2012, 22:54
MacFauz wrote:
1 & 2 together

a can be non zero while b and c could be 0. or
a can be 0 while b and c could be non zero. or
a,b & c all three can be 0.

So it is still not possible to determine whether a is zero or not.

Hence answer is E


Note: Look out for the case where b and c cannot be 0 at the same time. In that case, a must be 0.

e.g. the same question if slightly modified could result in (C)

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) (2a+10b-1)(2a-b-4)=0

From (1), (2a-b-4) = 0 OR (a+5b+2)=0 OR both are 0.
From (2), (2a-b-4)=0 OR (2a+10b-1)= 0 OR both are 0.

From no values of a and b, can (a+5b+2) and (2a+10b-1) be 0 simultaneously.
a + 5b + 2 = 0 implies a + 5b = -2
2a + 10b - 1 = 0 implies a + 5b = 1/2

a + 5b cannot take 2 different values at the same time. So (2a-b-4) must be 0.
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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 08 Jul 2017, 22:15
E is correct because there is an existence of a and b such that (a+5b+2) = 0 and (4a+3b-1) = 0. Also, the values of a and b in those 2 equations will not belong to a point on the line: y=2x-4
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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 08 Jul 2017, 23:45
Bunuel wrote:
Skientist wrote:
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


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.


hello Bunuel,
superb explanation, just one question though, Are we interested in getting a only a unique solution for a and b, and only then we can say definitely if (a,b) lies on the line segment or not?
Thanx
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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 10 Jul 2017, 20:39
saurabhsavant wrote:
Bunuel wrote:
Skientist wrote:
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


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.


hello Bunuel,
superb explanation, just one question though, Are we interested in getting a only a unique solution for a and b, and only then we can say definitely if (a,b) lies on the line segment or not?
Thanx


I believe the question is already obvious. The question is not about the unique value of a or b, but about whether any point (a,b) with the value satisfies the statement 1 or 2 will belong to the line
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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 09 Oct 2017, 14:56
VeritasPrepKarishma wrote:
MacFauz wrote:
1 & 2 together

a can be non zero while b and c could be 0. or
a can be 0 while b and c could be non zero. or
a,b & c all three can be 0.

So it is still not possible to determine whether a is zero or not.

Hence answer is E


Note: Look out for the case where b and c cannot be 0 at the same time. In that case, a must be 0.

e.g. the same question if slightly modified could result in (C)

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) (2a+10b-1)(2a-b-4)=0

From (1), (2a-b-4) = 0 OR (a+5b+2)=0 OR both are 0.
From (2), (2a-b-4)=0 OR (2a+10b-1)= 0 OR both are 0.

From no values of a and b, can (a+5b+2) and (2a+10b-1) be 0 simultaneously.
a + 5b + 2 = 0 implies a + 5b = -2
2a + 10b - 1 = 0 implies a + 5b = 1/2

a + 5b cannot take 2 different values at the same time. So (2a-b-4) must be 0.




this question is not modified, so the answer is "C" ?
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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 09 Oct 2017, 18:45
soodia wrote:
VeritasPrepKarishma wrote:
MacFauz wrote:
1 & 2 together

a can be non zero while b and c could be 0. or
a can be 0 while b and c could be non zero. or
a,b & c all three can be 0.

So it is still not possible to determine whether a is zero or not.

Hence answer is E


Note: Look out for the case where b and c cannot be 0 at the same time. In that case, a must be 0.

e.g. the same question if slightly modified could result in (C)

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) (2a+10b-1)(2a-b-4)=0

From (1), (2a-b-4) = 0 OR (a+5b+2)=0 OR both are 0.
From (2), (2a-b-4)=0 OR (2a+10b-1)= 0 OR both are 0.

From no values of a and b, can (a+5b+2) and (2a+10b-1) be 0 simultaneously.
a + 5b + 2 = 0 implies a + 5b = -2
2a + 10b - 1 = 0 implies a + 5b = 1/2

a + 5b cannot take 2 different values at the same time. So (2a-b-4) must be 0.




this question is not modified, so the answer is "C" ?


the correct answer is E, and btw, what do you mean by "the question is not modified"?
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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 10 Oct 2017, 05:45
soodia wrote:
VeritasPrepKarishma wrote:
MacFauz wrote:
1 & 2 together

a can be non zero while b and c could be 0. or
a can be 0 while b and c could be non zero. or
a,b & c all three can be 0.

So it is still not possible to determine whether a is zero or not.

Hence answer is E


Note: Look out for the case where b and c cannot be 0 at the same time. In that case, a must be 0.

e.g. the same question if slightly modified could result in (C)

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) (2a+10b-1)(2a-b-4)=0

From (1), (2a-b-4) = 0 OR (a+5b+2)=0 OR both are 0.
From (2), (2a-b-4)=0 OR (2a+10b-1)= 0 OR both are 0.

From no values of a and b, can (a+5b+2) and (2a+10b-1) be 0 simultaneously.
a + 5b + 2 = 0 implies a + 5b = -2
2a + 10b - 1 = 0 implies a + 5b = 1/2

a + 5b cannot take 2 different values at the same time. So (2a-b-4) must be 0.




this question is not modified, so the answer is "C" ?


If the question is modified (as discussed above), the answer would be (C).
For the unmodified question, the answer would be (E).
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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain  [#permalink]

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