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# On the xy plane region R consists of all points (x,y) such

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Manager
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On the xy plane region R consists of all points (x,y) such [#permalink]

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20 Sep 2006, 16:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
VP
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20 Sep 2006, 16:58
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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20 Sep 2006, 18:01
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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20 Sep 2006, 18:37
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.

Manager
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20 Sep 2006, 21:37
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.

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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20 Sep 2006, 22:07
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.

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.
Senior Manager
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20 Sep 2006, 22:21
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.

i do not understand this...
Manager
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21 Sep 2006, 00:31
This is a bizarre question because each statement gives sufficient, but conflicting answers. Going with D, but donâ€™t think such a question would ever come on the actual GMAT.
SVP
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21 Sep 2006, 01:38
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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21 Sep 2006, 04:07
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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21 Sep 2006, 04:13
Thanks .... I have corrected some mistakes and added some forgotten words since
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21 Sep 2006, 07:12
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.

i do not understand this...
Manager
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21 Sep 2006, 15:59
I chose B but OA is E.

Does anyone agree with the OA? or do you think the OA is mistaken.
Senior Manager
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21 Sep 2006, 16:34
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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21 Sep 2006, 16:44
I confirm.

2x+3y = 6
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21 Sep 2006, 18:19
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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22 Sep 2006, 01:01
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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