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Manager  Joined: 02 May 2012
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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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4
9
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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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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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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Got it buddy !!
Kudos for you .. 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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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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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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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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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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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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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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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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_________________ Re: In the xy-plane, does the line with the equation y = 2x - 4 contain   [#permalink] 12 Apr 2019, 05:20
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