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x-y plane

by karthikpandian19 » Tue Nov 08, 2011 8:26 pm
In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r<=3 & s<=2

What is answer for this Data Sufficiency question?
Last edited by karthikpandian19 on Wed Nov 09, 2011 10:42 pm, edited 1 time in total.
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by user123321 » Tue Nov 08, 2011 8:33 pm
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
1) clearly (r,s) lies on 3x+2y = 6 for sure but it can or may not be on 2x + 3y = 6(since these two lines are not parallel there will a point (r,s) which lies on both but rest of the points lie on 3x+2y = 6). hence insufficient.
2) (3,2) clearly does not lie on 2x + 3y =6. hence sufficient.

[spoiler]is it B?[/spoiler]

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by karthikpandian19 » Tue Nov 08, 2011 8:50 pm
user123321 wrote:
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
1) clearly (r,s) lies on 3x+2y = 6 for sure but it can or may not be on 2x + 3y = 6(since these two lines are not parallel there will a point (r,s) which lies on both but rest of the points lie on 3x+2y = 6). hence insufficient.
2) (3,2) clearly does not lie on 2x + 3y =6. hence sufficient.

[spoiler]is it B?[/spoiler]

user123321
OA is E....but i am not sure about the explanation.
Can someone explain the answer????
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by user123321 » Tue Nov 08, 2011 9:00 pm
karthikpandian19 wrote:
user123321 wrote:
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
1) clearly (r,s) lies on 3x+2y = 6 for sure but it can or may not be on 2x + 3y = 6(since these two lines are not parallel there will a point (r,s) which lies on both but rest of the points lie on 3x+2y = 6). hence insufficient.
2) (3,2) clearly does not lie on 2x + 3y =6. hence sufficient.

[spoiler]is it B?[/spoiler]

user123321
OA is E....but i am not sure about the explanation.
Can someone explain the answer????
I think B should be answer for this one as per the logic i mentioned.
Can you check the question, if you had missed any additional data or not.

Thanks,
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by pemdas » Tue Nov 08, 2011 9:38 pm
the very easy solution here would be in st(1) 3r+2s=6 and we have slope=-3/2 from s=-3r/2 +3. Our question suggests slope=-2/3 from y=-2x/3 + 2.
Our answer is that two lines cross at some point - they may have point in common (at least one) and may not have. The lines are not parallel, i.e. slopes are different.
Not Sufficient.
st(2) r=3 and s=2, we are missing data to define a slope here. Only one point is given and to find the slope we need at least two points. Not Sufficient

Combined st(1) we have slope information and points per r and s, but this is Not Sufficient to define that we have parallel lines with equal slopes. Hint: in st(1) we already found that the slope for (r,s) is different from that of (x,y) no need to dig further here (unlike tricky GMAT med-to hard difficulty level questions)
e

we need slope information in general to understand if lines are ||. If they are then we could have either all lines of (x,y) are on (r,s) or no common points can be found on two lines. But even with || lines we would need to find intercept information too, to understand which is which
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
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by Anurag@Gurome » Tue Nov 08, 2011 10:13 pm
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
Discussed earlier: https://www.beatthegmat.com/xy-plane-t87947.html
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by user123321 » Wed Nov 09, 2011 4:00 am
the second option you posted in the problem didn't have inequality symbols, that's why didnt get E as answer.

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by pemdas » Wed Nov 09, 2011 10:07 pm
@karthikpandian19: Please edit the question. Most BTG members aspire solving questions on this forum before searching the net for ready solutions and meaningless copy/paste of answers. It's waste of our time and energy to post the mis-typos and inaccurate text here.
:(
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2

What is answer for this Data Sufficiency question?
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by GMATGuruNY » Thu Nov 10, 2011 1:31 am
karthikpandian19 wrote:In the xy plane, region R consists of all the points (x,y) such that 2x + 3y ≤ 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r≤3 & s≤2

What is answer for this Data Sufficiency question?
I've amended the question to reflect how it appears in the OG12.

Question rephrased: Is 2r+3s≤6?

Try to plug in values that satisfy both statements.
Maximize r in one case and s in the other.

r maximized:
Let r=3 and s=0.
Statement 1 is satisfied: 3(3)+2(0)=6.
Statement 2 is satisfied: 3≤3 and 0≤2.
Is 2(3) + 3(0) ≤ 6? YES.

s maximized:
Let r=2/3 and s=2.
Statement 1 is satisfied: 3(2/3)+2(2)=6.
Statement 2 is satisfied: 2/3≤3 and 2≤2.
Is 2(2/3) + 3(2) ≤ 6? NO.

Since in the first case the answer is YES and in the second case the answer is NO, INSUFFICIENT.

The correct answer is E.
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by pemdas » Thu Nov 10, 2011 4:07 am
say the question looks as it was originally posted by an author, the answer would be E and not B still.
In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2
my solution above to the erroneously posted question is similar in method to that of Anurag. The difference is that in Anurag's solution the graph has been plotted too. If we know about slopes - positive, negative, we may describe them graphically - the upper and lower ceilings of the left and right sides of x-y for negative slopes, i.e. I and III quadrants. The essence is in their not being parallel, hence directed differently with one (since the function is linear) cross point in the plain.
user123321 wrote:the second option you posted in the problem didn't have inequality symbols, that's why didnt get E as answer.

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by user123321 » Thu Nov 10, 2011 5:24 am
pemdas wrote:say the question looks as it was originally posted by an author, the answer would be E and not B still.
In the xy plane, region R consists of all the points (x,y) such that 2x + 3y = 6. Is the points (r,s) in region R?

1. 3r+2s=6
2. r=3 & s=2
my solution above to the erroneously posted question is similar in method to that of Anurag. The difference is that in Anurag's solution the graph has been plotted too. If we know about slopes - positive, negative, we may describe them graphically - the upper and lower ceilings of the left and right sides of x-y for negative slopes, i.e. I and III quadrants. The essence is in their not being parallel, hence directed differently with one (since the function is linear) cross point in the plain.
user123321 wrote:the second option you posted in the problem didn't have inequality symbols, that's why didnt get E as answer.

user123321
@pemdas
if we know the point is (r,s) = (3,2) then we can clearly say that (r,s) is not on 2x+3y = 6. hence B is sufficient. I think user missed the inequality sign in line equation as well :).

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re

by pemdas » Thu Nov 10, 2011 3:38 pm
I know it's missing info, and in anyway the dispute is outstretching, but my point re selecting E and not B is that we cannot assume r and s to be fixed to the given values, rather we may consider these as one point of some function of r from s => f(r)=s. Thus by taking one value for r and s always you assume not the line but one point only. I see here function, f(r) and (r,s) can still be on and out of the given line region R. You assumed (r,s) is one point and not line, otherwise why r and s cannot be other values. But to come up with line equation we would need to know one more point and define the slope, which we could not do here, hence B is not sufficient.
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