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.
Pls explain the step and the logic to solve similar type of problems.
y=3x+2 - point (r,s)
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If the point (r, s) is on the line y = 3x + 2, then r = 3r + 2 ---> (3r + 2 - s) = 0vishal_2804 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
So the question reduces to "Is (3r + 2 - s) = 0?"
Statement 1: (3r + 2 - s)(4r + 9 - s) = 0
So, either (3r + 2 - s) = 0 OR (4r + 9 - s) = 0
Not sufficient
Statement 2: (4r - 6 - s)(3r + 2 - s) = 0
So, either (4r - 6 - s) = 0 OR (3r + 2 - s) = 0
Not sufficient
1 & 2 Together: Either {(4r + 9 - s) = 0 and (4r - 6 - s) = 0} OR (3r + 2 - s) = 0
Now, if (4r + 9 - s) = 0 and (4r - 6 - s) = 0
--> (4r - s) = -9 and (4r - s) = 6
--> This is not possible for any values of r and s
So, (3r + 2 - s) must be equal to zero.
Sufficient
The correct answer is C.
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If (r,s) is on the line defined by the equation y=3x+2, then (r,s) must satisfy the equation y=3x+2. In other words, it must be true that s=3r+2vishal_2804 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.
For example: We know that the point (5, 17) is on the line y=3x+2, because when we plug x=5 and y=17 into the equation, we get 17 = 3(5)+2 and the equation holds true.
So, we can reword the target question to be "Does s = 3r + 2?"
1. (3r+2-s)(4r+9-s) = 0
From this, we know that either (3r+2-s) = 0 or (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our new target question is no
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT
2. (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our new target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT
Statements 1&2 combined: Since (3r+2-s) is the only expression common to both statements, it must be true that 3r+2-s = 0, in which case s MUST equal 3r+2
As such the answer is C
Cheers,
Brent
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Question is whether point (r,s) lies on RED line ?
St1: Either point (r,s) lies on RED line or GREEN line.
Not sufficient
St2: Either point (r,s) lies on RED line or BLUE line.
Not sufficient
Together: Only possible scenario is that the point lies on red line. No one point can possibly lie on both the green and blue line because they are parallel. They will never intersect each other.
Hence Point (r,s) lies on RED line.
SUFFICIENT
Ans C
St1: Either point (r,s) lies on RED line or GREEN line.
Not sufficient
St2: Either point (r,s) lies on RED line or BLUE line.
Not sufficient
Together: Only possible scenario is that the point lies on red line. No one point can possibly lie on both the green and blue line because they are parallel. They will never intersect each other.
Hence Point (r,s) lies on RED line.
SUFFICIENT
Ans C
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- jervizeloy
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Hi Brent,Brent@GMATPrepNow wrote:If (r,s) is on the line defined by the equation y=3x+2, then (r,s) must satisfy the equation y=3x+2. In other words, it must be true that s=3r+2vishal_2804 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.
For example: We know that the point (5, 17) is on the line y=3x+2, because when we plug x=5 and y=17 into the equation, we get 17 = 3(5)+2 and the equation holds true.
So, we can reword the target question to be "Does s = 3r + 2?"
1. (3r+2-s)(4r+9-s) = 0
From this, we know that either (3r+2-s) = 0 or (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our new target question is no
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT
2. (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our new target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT
Statements 1&2 combined: Since (3r+2-s) is the only expression common to both statements, it must be true that 3r+2-s = 0, in which case s MUST equal 3r+2
As such the answer is C
Cheers,
Brent
Just a minor question that does not change the result but would be of great help to reinforce my concepts.
I think for each statement there are three cases to analyze. For example, for statement 1 we would have:
3r+2-s=0
OR
4r+9-s=0
OR
3r+2-s=0 AND 4r+9-s=0
Would such analysis be correct?
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Yes, that's a correct analysis.jervizeloy wrote: Hi Brent,
Just a minor question that does not change the result but would be of great help to reinforce my concepts.
I think for each statement there are three cases to analyze. For example, for statement 1 we would have:
3r+2-s=0
OR
4r+9-s=0
OR
3r+2-s=0 AND 4r+9-s=0
Would such analysis be correct?
Cheers,
Brent
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This is true, but the cases are different in an important way. The first two give you r in terms and s, and the last one gives you the exact values of r and s. So depending on the prompt, the first two might be sufficient, or you might need the third case.jervizeloy wrote: I think for each statement there are three cases to analyze. For example, for statement 1 we would have:
3r+2-s=0
OR
4r+9-s=0
OR
3r+2-s=0 AND 4r+9-s=0
Would such analysis be correct?