In the xy-plane, region R consists of all the points (x.y) : DS Archive
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# In the xy-plane, region R consists of all the points (x.y)

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15 Feb 2005, 23:22
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In the xy-plane, region R consists of all the 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

Last edited by DLMD on 16 Feb 2005, 08:53, edited 1 time in total.
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16 Feb 2005, 01:55
I assumed that there was a mistake in statement 1, it should be
(1) 3r + 2s = 6
if not it doesn't seem correct, r is an abscyss and x too

I would choose B because statement 1 just tell us the equation of one line and not where is the point (r,s).

With statement1, we can see that the line with equation 3r + 2s = 6 is crossing the line with equation 2x + 3y = 6 so there is one common point that can satisfy both equation but we don't know if (r,s) is this point or any other.

statement 2 let us know where is the point and it's clearly not in the line with equation 2x + 3y = 6 so we can answer NO

However, I am confused, I am not sure one single line can be considered as a region, I thought a region would have been defined more like 2x + 3y > 6 or 2x + 3y < 6
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16 Feb 2005, 01:57
I m not sure I understand the question completely.

However seems like D is the answer.

Question Stem. Substitute x=0 and y=0 and coordinates are
(0,2) and (3,0)

1. 3r+2x=6
Replace x=0, r=2 Sufficient

2. r=3, s=2
Not a part of region. Sufficient

What is the OA?
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16 Feb 2005, 02:18
DLMD wrote:
In the xy-plane, region R consists of all the points (x.y) such that 2x + 3y = 6. Is the point (r,s) in region R?

(1) 3r + 2x = 6

(2) r=3 and s=2

i think it shud be 2r+3s = 6...stll with it we get D(ST1:YES, ST2:NO)
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16 Feb 2005, 07:15
"B" it is.

For (r,s) to lie in the region 2r+3s = 6

I. shud be 3r+2s = 6.....for r = 6/5 and s = 6/5....it satisfies both eqn, but r = 1 and s = 3/2....it satifies 3r+2s = 6 but not 2r+3s = 6....insuff

II. r = 3 and s = 2.....6+6 = 12....doesn't satisfy....suff
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16 Feb 2005, 07:41
I go with statement one being sufficient
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16 Feb 2005, 08:54
Antmavel wrote:
I assumed that there was a mistake in statement 1, it should be
(1) 3r + 2s = 6
if not it doesn't seem correct, r is an abscyss and x too

I would choose B because statement 1 just tell us the equation of one line and not where is the point (r,s).

With statement1, we can see that the line with equation 3r + 2s = 6 is crossing the line with equation 2x + 3y = 6 so there is one common point that can satisfy both equation but we don't know if (r,s) is this point or any other.

statement 2 let us know where is the point and it's clearly not in the line with equation 2x + 3y = 6 so we can answer NO

However, I am confused, I am not sure one single line can be considered as a region, I thought a region would have been defined more like 2x + 3y > 6 or 2x + 3y < 6

sorry for the typo, I just edited.
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16 Feb 2005, 08:55
my answer is B, but OA is E, any thoughts?
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16 Feb 2005, 09:15
I think the reason the answer is E because nowhere in the qtn(I am assuming that is the full text of the qtn) have they defined Region R. By assuming that R is the region formed by the X axis, y axis and this third line we have all erred.

I guess So!!!!!
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16 Feb 2005, 09:18
swath20 wrote:
I think the reason the answer is E because nowhere in the qtn(I am assuming that is the full text of the qtn) have they defined Region R. By assuming that R is the region formed by the X axis, y axis and this third line we have all erred.

I guess So!!!!!

I believe OA is wrong, ques says that the straight line in XY plane creates a region, a region doesn't neccessarily have to have 2 lines, curve etc. A straight line is a region as well, however infinitely small it may be.
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16 Feb 2005, 11:05
Just a question but can you define a plan by an equation for a line? If you plot the equation 2x+3y = 6 you get a line through which can draw an infinite number of planes right? SO unless (r,s) is on the line itself you really cannot know if it is on the plane right? Could that be why the answer is E?
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16 Feb 2005, 13:30
I go with B, since the region R is defined by a straight line, and r,s is on this line.

statement 1 is not enough to say that (r,s) is on the same line as (x,y) since it defines a different line. It may intersect with R but it's not certain with just statement 1. Statement 2 gives a set of values for r,s so we know for sure it's on R.
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16 Feb 2005, 19:04
DLMD wrote:
Vijo wrote:
DLMD can you plz post the OE.

I don't have OE, only OA

plz let me know the question no. ill find it out
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28 Feb 2005, 18:29
DLMD wrote:
In the xy-plane, region R consists of all the 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

I also came out with b
1. point (r, s) may or may not be in region R, as these two lines do in fact intersect -- insufficient
2. point's exact coordinates are revealed, so this is sufficient

I think it's important that we get to the bottom of this question
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02 Mar 2005, 10:19
It's B. Can I ask for the source?
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02 Mar 2005, 10:42
gter wrote:
I go with B, since the region R is defined by a straight line, and r,s is on this line.

statement 1 is not enough to say that (r,s) is on the same line as (x,y) since it defines a different line. It may intersect with R but it's not certain with just statement 1. Statement 2 gives a set of values for r,s so we know for sure it's on R.

That's what I thought too. Doesn't the 1st statement just give another line and not any information about what points r and s are?
02 Mar 2005, 10:42
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