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On the xy plane region R consists of all points (x,y) such [#permalink]
 20 Sep 2006, 16:17
On the xy plane region R consists of all points (x,y) such that 2x+3y=6.
Is the point (r,s) in region R?
(1) 3r+2s=6
(2) r = 3 and s= 2
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VP
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Go for D here
1) x can be 2/3r y can be 3/2s
2) since that point is not on the given eq 2x+3y=6. We can sya that its not on the line
So D
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Manager
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Why woudn't it be B?
statement one gives us an equation, but we can't solve for both variables...so we can't see if its on the line.
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Given line :
2x+3y= 6
S1:
2r+3s = 6
If r=0, s = 2, (0,2) on the line.
This is sufficient to determine if point is on the line.
S2: r = 3, s = 2
Sufficient.
Answer: D
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haas_mba07 wrote: Given line :
2x+3y= 6
S1:
2r+3s = 6
If r=0, s = 2, (0,2) on the line.
This is sufficient to determine if point is on the line.
S2: r = 3, s = 2
Sufficient.
Answer: D
Do you mean to say that (r,s) is on the line?
I too think D is the answer, but my calculations say that the point is not on the line.
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VP
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You could come up with values of r,s to find out if it is on the line. But either way the equation is sufficient to determine if the point is on the line... I was trying to practice saving some time on computing the solution..  Or maybe just lazy
Priyah wrote: haas_mba07 wrote: Given line :
2x+3y= 6
S1:
2r+3s = 6
If r=0, s = 2, (0,2) on the line.
This is sufficient to determine if point is on the line.
S2: r = 3, s = 2
Sufficient.
Answer: D Do you mean to say that (r,s) is on the line? I too think D is the answer, but my calculations say that the point is not on the line. |
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haas_mba07 wrote: Given line :
2x+3y= 6
S1:
2r+3s = 6
If r=0, s = 2, (0,2) on the line.
This is sufficient to determine if point is on the line.
S2: r = 3, s = 2
Sufficient.
Answer: D
i do not understand this...
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Manager
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This is a bizarre question because each statement gives sufficient, but conflicting answers. Going with D, but don’t think such a question would ever come on the actual GMAT.
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Get (B)
The equation is actually the one of the line (L) represented by y=-2*x/3+2
Statement (1) : 3r+2s=6
This is actually another line (K) such as y = -3*x/2 + 3
As we can see, The slops of (L) and (K) are not equal. Thus, the 2 lines intersect at 1 point only. Hence, we can have the point (r,s) on (L) or not on (L).
INSUFF
Statement (2) : r = 3 and s= 2
This gives us enough information to conclude without calculating. These values have to verify the equation of the line (L).
SUFF
Last edited by Fig on 21 Sep 2006, 04:12, edited 2 times in total.
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VP
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Fig wrote: Get (B)
The equation is actually the one of the line (L) represented by y=-2*x/3+2
Statement (1) : 3r+2s=6
This is actually another line (K) such as y = -3*x/2 + 3
As we can see, The slops of (L) and (K) are not equal. Thus, the 2 lines intersect at 1 point only. Hence, we can the point (r,s) on (L) or not on (L).
INSUFF
Statement (2) : r = 3 and s= 2
This gives us enough information to conclude without calculating. These value have to verify the equation of the line (L).
SUFF
Awesome 
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Thanks .... I have corrected some mistakes and added some forgotten words since 
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VP
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Yep! Flipped it around... 
iced_tea wrote: haas_mba07 wrote: Given line :
2x+3y= 6
S1:
2r+3s = 6
If r=0, s = 2, (0,2) on the line.
This is sufficient to determine if point is on the line.
S2: r = 3, s = 2
Sufficient.
Answer: D i do not understand this... |
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Manager
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I chose B but OA is E.
Does anyone agree with the OA? or do you think the OA is mistaken.
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Senior Manager
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I think there is some thing wrong with the question here. when we talk about a region shouldn't the equation be something like this
2x+3y>=6 or 2x+3y<=6 or 2x+3y<6 etc
2x+3y=6 is straight line and it cannot represent a region. Positive can you check the question again ?
If thats the case the answer could be E . What do you guys think ?
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Manager
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I confirm.
2x+3y = 6
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VP
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Is it E 'cos (r,s) may or may not be in xy plane?
B sounded logical after I chose D.
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trivikram wrote: Is it E 'cos (r,s) may or may not be in xy plane?
B sounded logical after I chose D.
It's (B) because,in statment 1, we have 2 lines that intersect on 1 common point.
In other words, a point A(r,s) can be choosen on R or not on R (the commong point or another point of the line 3r+2s=6<=>y = -3*x/2 + 3 ).
Hope this help
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