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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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19 Oct 2012, 11:13
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Dec 2017, 23:18, 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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19 Oct 2012, 11:40
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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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21 Oct 2012, 01:48
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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21 Oct 2012, 04:54
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.

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

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21 Oct 2012, 05:18
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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23 Oct 2012, 21:54
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.

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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18108 [0], given: 236 VP Joined: 12 Dec 2016 Posts: 1340 Kudos [?]: 46 [0], given: 1358 Location: United States GMAT 1: 700 Q49 V33 GPA: 3.64 Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 08 Jul 2017, 21:15 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 Kudos [?]: 46 [0], given: 1358 Manager Joined: 27 Aug 2016 Posts: 95 Kudos [?]: 4 [0], given: 149 Location: India Schools: HEC Montreal '21 GMAT 1: 670 Q47 V37 GPA: 3 WE: Engineering (Energy and Utilities) Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 08 Jul 2017, 22:45 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 Kudos [?]: 4 [0], given: 149 VP Joined: 12 Dec 2016 Posts: 1340 Kudos [?]: 46 [0], given: 1358 Location: United States GMAT 1: 700 Q49 V33 GPA: 3.64 Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 10 Jul 2017, 19:39 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 Kudos [?]: 46 [0], given: 1358 Manager Joined: 30 Apr 2017 Posts: 88 Kudos [?]: 2 [0], given: 74 Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 09 Oct 2017, 13:56 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" ? Kudos [?]: 2 [0], given: 74 VP Joined: 12 Dec 2016 Posts: 1340 Kudos [?]: 46 [0], given: 1358 Location: United States GMAT 1: 700 Q49 V33 GPA: 3.64 Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 09 Oct 2017, 17:45 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"? Kudos [?]: 46 [0], given: 1358 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7791 Kudos [?]: 18108 [0], given: 236 Location: Pune, India Re: In the xy-plane, does the line with the equation y = 2x - 4 contain [#permalink] ### Show Tags 10 Oct 2017, 04:45 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). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: In the xy-plane, does the line with the equation y = 2x - 4 contain   [#permalink] 10 Oct 2017, 04:45
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