In the XY plane, does the line with equation y=3x+2 : GMAT Data Sufficiency (DS)
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# In the XY plane, does the line with equation y=3x+2

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In the XY plane, does the line with equation y=3x+2 [#permalink]

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04 Sep 2010, 05:35
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In the xy-plane , does the line with equation y=3x+2 contains the point(r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0
[Reveal] Spoiler: OA

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In the XY plane, does the line with equation y=3x+2 [#permalink]

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04 Sep 2010, 05:44
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In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ cannot be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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04 Sep 2010, 06:19
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Substituting (r,s) in the original equation:
y=3x+2 => s=3r+2 => 3r-s+2=0.
Question : is 3r-s-2=0. ??
statement 1 - (3r+2-s)(4r+9-s)=0 => (3r+2-s)=0 or (4r+9-s)=0
Not sufficient

Statement 2 - (4r-6-s)(3r+2-s)=0 => (3r+2-s)=0 or (4r-6-s)=0
Not sufficient
Combining 1&2 ->
common result (3r+2-s)=0
Sufficient.
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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04 Sep 2010, 07:50
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I took it totally wrong:
What i did was , from stmt 1:
1) (3r+2-s)(4r+9-s)=0
3r+2-s=0
4r+9-s=0 and equating both of them to find value of r and s.

Total disaster.

Thanks a lot guys ...Kudos to Bunuel and soumanag
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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05 Sep 2010, 08:55
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Bunuel - you make every question looks so simple. always awesome explanation.
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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10 Sep 2010, 09:55
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awesome explanation Bunuel and Soumanag......thanks....
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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10 Sep 2010, 10:00
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i was doing the same mistake of solving for r and s and then putting it in the original equation... thanks for the clarification.....
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Re: In the x-y plane [#permalink]

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18 Dec 2010, 21:09
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Quote:
In the x-y plane, does the line with equation y = 3x + 2 contain the point (r,s) ?

1. (3r + 2 - s) (4r + 9 - s) = 0

2. (4r -6 -s) (3r + 2 - s) = 0

y = 3x +2 will contain the point (r,s), if :
s = 3r +2 (substitute r for x and s for y , in the eqn of line) => if 3r+2 -s = 0 ?

Statement 1 :
(3r + 2 - s) (4r + 9 - s) = 0
=> either (3r + 2 -s) =0 or (4r +9 -s ) = 0 -> Not Sufficient

Statement 2 :
(4r -6 -s) (3r + 2 - s) = 0
=> either (4r -6 -s) = 0 or (3r + 2 -s ) = 0 -> Not sufficient

Combining them :

3r + 2 - s = 0 - Sufficient (As [4r -s +9] and [4r -s -6] both can't be zero at the same time, they have a difference of 15).

Hence , C.
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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19 Dec 2010, 05:41
Thanks a ton Bunuel!
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Re: Geometry - Hard [#permalink]

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09 Mar 2011, 21:05
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s = 3r + 2 should be true if equation y = 3x+2 contain the point (r,s)

From (1), s = 3r + 2 could be possible, but not sure

because 4r + 9 - s = 0 or 4r - s = -9 might be possible as well.

From(2), s = 3r + 2 could be possible, but not sure

because 4r - 6 - s = 0 or 4r - s = 6 might be possible as well.

However, from (1) and (2), only 3r + 2 - s = 0 can be true

else -9 = 6, which is absurd. So the answer is C.
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Re: Coordinate geometry - gmatprep [#permalink]

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10 Jan 2012, 07:17
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Ok.. So lets look at both the statements individually:

First Statement 1:

1. (3r+2-s)(4r+9-s)=0

Look at the statement. It could mean two things. Either (3r+2-s) = 0 or (4r+9-s) = 0

if (3r+2-s) = 0, then yes 3r+2-s = 0 and hence s=3r+2 which is exactly like saying y=3x+2

But if 3r+2-s is not equal to 0 then we don't know for sure.

Now lets look at statement 2:

2. (4r-6-s)(3r+2-s)=0

Same implies for statement 2.

now lets assume that in the first statement 4r+9-s=0. If that is true, then from the second statement it is not possible for 4r-6-s to be equal to 0. Hence 3r+2-s = 0 and yes the point r,s which is the same as x,y lies on it !

Hence C
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Re: Coordinate geometry - gmatprep [#permalink]

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10 Jan 2012, 12:06
Easy one. GMAT loves these type of patterns.

NOTE: Notice the pattern here. When you have similar type of information in both statements, the answer is usually C, D or E.

1. rephrasing the equations gives us s=3r+2 and s=4r+9. obviously s=4r+9 does not lie, but s=3r+2 does
2. rephrasing the equations gives us s=3r+2 and s=4r-5. obviously s=4r-5 does not lie, but s=3r+2 does

Together, s=3r+2 and it does lie. C.
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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20 Apr 2012, 05:25
Bunuel wrote:
In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ can not be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

Bunuel,

Again, sorry for re-opening an old thread but I have a small doubt regarding this question. I got this question on my GMAT Prep today, had one quick look at the options and immediately saw that for the point to lie on the line, 3r+2-s has to be equal to zero. And since this information was given to us in two separate quadratic equations, it was necessary for us to have both the equations in order to discard (4r+9-s) and (4r-6-s) as solutions to the given equations.

However, at this point, I thought to myself that C would be too easy an answer and solved the equations to see if GMAT was upto its usual trickery. And this is where I went wrong.

Take for example the first equation. One solution gives us what we want, i.e., 3r+2-s = 0. However, if we solve the second solution 4r+9-s = 0, we get s = 4r+9. Now, if we plug this into the original equation y = 3x+2, we get:

y = 3x+2
Plugging the values of r and s into x and y:

4r+9 = 3r +2;
Solving this gives us r = -7 and s = -19 and plugging these values of r and s in the original equation satisfies the equation:

-19 = 3(-7) + 2;
-19 = -19

Since, this equation too satisfies the equation (and similarly, so does the second equation) I marked the answer as D.

Can you please tell me where I am going wrong?

Many thanks in advance.
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Re: Question from GMAT prep: Co-ordinate geo [#permalink]

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20 Apr 2012, 07:14
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arjuntomar wrote:
Bunuel wrote:
In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ can not be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

Bunuel,

Again, sorry for re-opening an old thread but I have a small doubt regarding this question. I got this question on my GMAT Prep today, had one quick look at the options and immediately saw that for the point to lie on the line, 3r+2-s has to be equal to zero. And since this information was given to us in two separate quadratic equations, it was necessary for us to have both the equations in order to discard (4r+9-s) and (4r-6-s) as solutions to the given equations.

However, at this point, I thought to myself that C would be too easy an answer and solved the equations to see if GMAT was upto its usual trickery. And this is where I went wrong.

Take for example the first equation. One solution gives us what we want, i.e., 3r+2-s = 0. However, if we solve the second solution 4r+9-s = 0, we get s = 4r+9. Now, if we plug this into the original equation y = 3x+2, we get:

y = 3x+2
Plugging the values of r and s into x and y:

4r+9 = 3r +2;
Solving this gives us r = -7 and s = -19 and plugging these values of r and s in the original equation satisfies the equation:

-19 = 3(-7) + 2;
-19 = -19

Since, this equation too satisfies the equation (and similarly, so does the second equation) I marked the answer as D.

Can you please tell me where I am going wrong?

Many thanks in advance.

The question asks whether $$3r+2-s=0$$. Now, statement (1) says: $$(3r+2-s)(4r+9-s)=0$$, which means that either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both.

The above DOES NOT mean that we have a system of equations: $$3r+2-s=0$$ and $$4r+9-s=0$$. Because if it were so then you have an answer right away: $$3r+2-s=0$$. No wonder that when you solve it as a system you got the values of $$s$$ and $$r$$ which make $$3r+2-s$$ equal to zero: your whole starting point was that it does.

Hope it's clear.
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Re: In the xy-plane, does the line with equation y = 3x + 2 [#permalink]

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17 Jun 2012, 00:04
Stiv wrote:
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s) (4r + 9 - s) = 0
2) (4r - 6 - s) (3r + 2 - s) = 0

If the point lies on the line, then it will satisfy the line equation.
that is -> s = 3r + 2
or to say 3r + 2 - s = 0

From 1 we get.
(3r + 2 - s) = 0 or (4r + 9 - s) = 0. NS
As (r,s) can lie on both lines, or on any one of then.

From 2 we get.
(3r + 2 - s) = 0 or (4r - 6 - s) = 0. NS
As (r,s) can lie on both lines, or on any one of then.

Combining both, we have only one root common.
(3r + 2 - s) = 0.

Ans C
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Re: In the xy-plane, does the line with equation y = 3x + 2 [#permalink]

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17 Jun 2012, 04:09
Bunuel wrote:
Stiv wrote:
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s) (4r + 9 - s) = 0
2) (4r - 6 - s) (3r + 2 - s) = 0

Merging similar topics. Please ask if anything remains unclear.

I don't understand why, but when I search for this question in the search query I get no results.
Also, this is not the only case. This happens quite often.
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Re: In the xy-plane, does the line with equation y = 3x + 2 [#permalink]

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17 Jun 2012, 04:12
Stiv wrote:
Bunuel wrote:
Stiv wrote:
In the xy-plane, does the line with equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s) (4r + 9 - s) = 0
2) (4r - 6 - s) (3r + 2 - s) = 0

Merging similar topics. Please ask if anything remains unclear.

I don't understand why, but when I search for this question in the search query I get no results.
Also, this is not the only case. This happens quite often.

Try to search using key words of the question. For example I'd search for: "equation", "contain", and "point". Though it's not a big problem if you search and don't find a question, moderators will help you with that. So, don't worry about that.
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Re: In the XY plane, does the line with equation y=3x+2 [#permalink]

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07 Jul 2013, 23:53
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Re: In the XY plane, does the line with equation y=3x+2 [#permalink]

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08 Jul 2013, 02:59
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gaurav2k101 wrote:
In the xy-plane , does the line with equation y=3x+2 contains the point(r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

A*B=0==>THEN EITHER A/B IS ZERO OR BOTH ARE ZERO...this is a rule.
now if r,s lies on point y=3x+2==>then 3r+2-s=0
now lets say 3r+2-s=A..
4r+9-s=B
4r-6-s=C

now statement 1 SAYS that ...A*B=0===>Clearly we are not sure that A=0 or not
similarly statement 2 says that ...A*C===>AGAIN WE CANNOT GAURANTEE THAT A=0..

NOW combining both we cam clearly say that A=0..
HENCE SUFFICIENT.
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Re: In the XY plane, does the line with equation y=3x+2 [#permalink]

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30 Aug 2013, 14:41
Bunuel,

In statement (1), you have said that we have these possibilities:
(3r + 2 - s) = 0 OR (4r + 9 - s) = 0 OR both.

But, when we have something like this:
(x + 3)(x+5) = 0

In this case, there are only two possibilities, right? (x+3)=0 OR (x+5)=0.
Both cannot be zero at the same time because "x" represents a single and unique value.
Re: In the XY plane, does the line with equation y=3x+2   [#permalink] 30 Aug 2013, 14:41

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