I honestly could not understand the question at all.
What I am supposed to do?
Solve the equations given in statements and check if they fit into the line equation ? or take relationship of r & s from line equation and put them into statement to see if it fits?
In the xy-plane, does the line...
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- GMATGuruNY
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If (r,s) is a point on the line y = 3x + 2, then s = 3r + 2, and 3r - s = -2. Thus, the question can be rephrased:In the xy-plane, does the line with equation y=3*X +2 contain the point (r,s) ?
(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0
Does 3r - s = -2?
Statement 1: (3r+2-s)(4r+9-s) = 0
Either 3r+2-s = 0 or 4r+9-s = 0.
If 3r+2-s = 0, then 3r - s = -2.
If 4r+9-s = 0, then 4r - s = -9 and 3r - s = ANY VALUE.
INSUFFICIENT.
Statement 2: (4r-6-s)(3r+2-s) = 0
Either 4r-6-s=0 or 3r+2-s = 0.
If 3r+2-s = 0, then 3r - s = -2.
If 4r-6-s = 0, then 4r -s = -6 and 3r - s = ANY VALUE.
INSUFFICIENT.
Statements 1 and 2 combined:
4r - s = -9 (from statement 1) and 4r - s = 6 (from statement 2) cannot both be true, since 4r - s cannot be equal to more than one value.
Thus, the only way that the equations in the two statements can both be equal to 0 is if 3r+2-s = 0, implying that 3r - s = -2.
SUFFICIENT.
The correct answer is C.
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- OptimusPrep
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Required: Does the line with equation y=3*X +2 contain the point (r,s)nchaswal wrote:
In the xy-plane, does the line with equation y=3*X +2 contain the point (r,s) ?
(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0
I honestly could not understand the question at all.
What I am supposed to do?
Solve the equations given in statements and check if they fit into the line equation ? or take relationship of r & s from line equation and put them into statement to see if it fits?
Or simply put, Is 3r - s +2 = 0?
Statement 1: (3r + 2 - s)(4r + 9 - s) = 0
This means either
(3r + 2 - s) = 0
Or (4r + 9 - s) = 0
INSUFFICIENT
Statement 2: (4r - 6 - s)(3r + 2 - s) = 0
This means either
(4r - 6 - s) = 0
Or (3r + 2 - s) = 0
INSUFFICIENT
Combining both statements:
We know that (3r + 2 - s) = 0
SUFFICIENT
Correct Option: C
For such questions, you should take relationship of r & s from line equation and put them into statement to see if it fits
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- Brent@GMATPrepNow
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One more solution to show that rephrasing the target question works in many (slightly) different forms:
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
Target question: Does the line with equation y = 3x + 2 contain the point (r,s)
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 + 2
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 REPHRASE the target question as "Does s = 3r + 2?"
Statement 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 REPHRASED target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our REPHRASED target question is no
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 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 REPHRASED target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our REPHRASED target question is yes
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Since (3r+2-s) is the only expression common to BOTH equations, it MUST be true that 3r+2-s = 0, in which case s MUST equal 3r+2
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
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Yeah, you have the right idea. If (r, s) is on the line, then its x-coordinate (which has value r) and its y-coordinate (which has value s) must satisfy the line equation. In other words, we'd neednchaswal wrote:I honestly could not understand the question at all.
What I am supposed to do?
Solve the equations given in statements and check if they fit into the line equation ? or take relationship of r & s from line equation and put them into statement to see if it fits?
s = 3r + 2
to be true.
- renatofarias
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Hi everyone. I did not understand why each statement is not true by itself.
I followed the instructions in the beggining reaching s = 3r + 2. So I went to substitute s in the Statements:
(1) (3r + 2 - s)(4r + 9 - s) = 0
When I reached (3r + 2 - (3r + 2))(4r + 9 - (3r + 2)) = 0 I wento on to say that the equation was true, thus making (r, s) part of the line.
The same for statement (2)
The question is, why does (r, s) have to satisfy "both parenthesis" if satisfying one should be enough to make the equation true?
Thank you very much
I followed the instructions in the beggining reaching s = 3r + 2. So I went to substitute s in the Statements:
(1) (3r + 2 - s)(4r + 9 - s) = 0
When I reached (3r + 2 - (3r + 2))(4r + 9 - (3r + 2)) = 0 I wento on to say that the equation was true, thus making (r, s) part of the line.
The same for statement (2)
The question is, why does (r, s) have to satisfy "both parenthesis" if satisfying one should be enough to make the equation true?
Thank you very much
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Think of a simple example with the same logic. Imagine the following question "Is x = 2?"renatofarias wrote:Hi everyone. I did not understand why each statement is not true by itself.
I followed the instructions in the beggining reaching s = 3r + 2. So I went to substitute s in the Statements:
(1) (3r + 2 - s)(4r + 9 - s) = 0
When I reached (3r + 2 - (3r + 2))(4r + 9 - (3r + 2)) = 0 I wento on to say that the equation was true, thus making (r, s) part of the line.
The same for statement (2)
The question is, why does (r, s) have to satisfy "both parenthesis" if satisfying one should be enough to make the equation true?
Thank you very much
If you had a statement that read (x - 2)(x + 4) = 0, you'd determine that x could be 2 or x could be -4, so because you could get a YES or a NO, the statement alone would not be sufficient to answer the question.
But if you plugged x = 2 into the equation, you'd get (2 - 2)(2 +4) = 0, which of course, is true. But it doesn't make the statement sufficient, right? (Remember x could be -4 too.) The issue is that we're not testing to see if the statement is true, given the initial question. We're testing to see if we can answer the original question, given a statement, which we have to take as true.
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(Similarly, if you're given (3r + 2 - s)(4r + 9 - s) = 0, it could be the case that 3r + 2 - s = 0, but it could also be true that 4r + 9 - s = 0. The concept is the same, it's just that the expressions are slightly more complicated in this example.)