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OG 13- DS- Q 129

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OG 13- DS- Q 129

by Suz » Thu Aug 09, 2012 10:52 pm
Hi,

Can someone help me with this problem? I didn't really understand the explanation in the OG


Q. 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



Thanks
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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Aug 09, 2012 10:54 pm
Suz wrote:Hi,

Can someone help me with this problem? I didn't really understand the explanation in the OG


Q. 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

Thanks
(1) 3r + 2s = 6 may or may not lie in region R. So, (1) is NOT SUFFICIENT to answer the question.

(2) If we take r = 3 and s = 2, then the point (3, 2) does not lie in region R.
r ≤ 3 and s ≤ 2 implies we can also take negative values for r and s. If r = -2, s = -3, then (-2, -3) lies in region R.
We don't get a unique answer, so (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), if r = 2, s = 0 then (2, 0) lies in region R. But if r = 2/3 and s = 2 then (2/3, 2) lies above the line 2x + 3y = 6, which means (2/3, 2) does not lie in region R. Combining also doesn't give a unique answer.

The correct answer is E.

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by dellaboemia » Fri Aug 24, 2012 8:41 am
Hello Dr. Mairal,

Would there be an algebraic solution to this problem?

- Della
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by GMATGuruNY » Fri Aug 24, 2012 9:16 am
I posted a solution here:

https://www.beatthegmat.com/xy-plane-and ... 97228.html
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