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Master | Next Rank: 500 Posts
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by arocks » Sat Oct 06, 2007 1:04 am
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 got the answer but is there a quick way for solving this. Thanks.
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Source: — Data Sufficiency |
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by samirpandeyit62 » Sat Oct 06, 2007 2:24 am
1) 3r + 2s = 6

slope of 2x + 3y =6 is -2/3 & slope of 3r + 2s= 6 is -3/2 hence they are not parallel so they will meet at a pt where x,y =r,s but otherwise x,y will not be equal to r,s so INSUFF

(2) r = 3 and s = 2 this pt does not satisfy the line eqn of
2x+3y =6 hence does not lie in the region SUFF

ans B
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Samir
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by arocks » Sat Oct 06, 2007 10:48 am
Got it...but the OA is E.
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by samirpandeyit62 » Sat Oct 06, 2007 11:44 am
Hi arocks,
well 2x + 3y = 6 is a line & (3,2) is a pt so this pt can either lie on the line or not, if it lies on the line then it will satisfy the eqn of the line else not, so here it does not satisfy the eqn so it does not lie on the line, now if we say that this is Insufficient, then it wud be because the pt may lie on the line or not which would be possible only if the region is changing i.e there are two or more line equations. How can one pt lie on a line & then lie outside(not on the line)
If the OA is E, can anyone explain how the stmt 2 is INSUFF
Regards
Samir
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by arocks » Sat Oct 06, 2007 12:35 pm
Makes sense....thanks.
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