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

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In the xy-plane, region R consists of all the points (x, y) [#permalink]  17 Sep 2008, 09:49
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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
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Re: DS-Cordinate Geometry [#permalink]  17 Sep 2008, 09:59
vivektripathi 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

IMO E

R consists of all the points that satisfy 2x + 3y = 6
R can consis of other points also ,hence (1) and (2) are not SUFFI

IMO E
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Re: DS-Cordinate Geometry [#permalink]  17 Sep 2008, 11:10
cant we put r = 3 and s = 2 in the equation 2x + 3y = 6 and see if it satisfied it.

and similarly see if same points satisfy the equation in A and the one in the q.

what am i missing?

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Re: DS-Cordinate Geometry [#permalink]  17 Sep 2008, 13:38
(r,s) must satisfy 2r+3s = 6 if it is in region R (I don't think the question implies that R could contain other points than those on this line).

(1) => 3r +2s =6 but we want to know if 2r +3s = 6 . This is true if (r,s) = (6/5,6/5), and false otherwise... INSUFF.

(2) => 2(3) + 3(2) = 12 which isn't equal to 6. This tells us (r,s) isn't in R. SUFF.

IMO : (B)
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Re: DS-Cordinate Geometry [#permalink]  17 Sep 2008, 22:07
Region R essentially means all the points on the line 2x + 3y = 6. If, I plot this line in XY plane, it will meet X-axis at (3,0) and Y-axis at (0,2).

Now stmt1 gives a line that meets X-axis at (2,0) and Y-axis at (0,3). This line definitely intersects the original line at one point. Hence, this is insufficient as only for one combination of r and s, this satisfies the original equation. For other combinations, it does not.

stmt 2: this is a point clearly not on the original line. Hence, sufficient.

Hence, B.
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Re: DS-Cordinate Geometry [#permalink]  18 Sep 2008, 06:50
Hi Vivek,

Well answer cannot be E at least when stmt 2 clearly says (r,s) doesnt lie on R
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Re: DS-Cordinate Geometry [#permalink]  18 Sep 2008, 07:20
vivektripathi 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

Looks like we are missing something in this question..

region R consists of all the points (x, y) such that 2x + 3y = 6
-- this is line not a region.. so I believe we are missing <= or >= then it may be region.
( 2x + 3y <= 6 or 2x + 3y >= 6 represents region)
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Re: DS-Cordinate Geometry [#permalink]  18 Sep 2008, 07:27
The equation 2x + 3y = 6 represent the line, it can not represent the region........
question itself might be wrong.....however it appeared to me as it is and that's why i could not understood it. the source is unknowm (some papers in PDF Form)

Last edited by vivektripathi on 18 Sep 2008, 09:47, edited 1 time in total.
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Re: DS-Cordinate Geometry [#permalink]  18 Sep 2008, 07:37
vivektripathi wrote:
The equation 2x + 3y = 6 represent the line, it can not represent the region........
question itself might be wrong.....however it appeared to as it is and that's why i could understood it.

What is the source of this question?
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Re: DS-Cordinate Geometry   [#permalink] 18 Sep 2008, 07:37
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