GMAC Focus question- DS (Linear plane)

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phillyguy_007: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Jun 11, 2007 8:12 am

by phillyguy_007 » Mon Dec 22, 2008 9:12 am

What is the fastest way to approach the following question?

In the xy plane, Region R consists of all points (x,y) such that 2x+3y<or=6. Is the point (r,s) in Region R?

(1) 3r+2s=6
(2) r<or=3 and s<or=2

Answer is......E.

Thanks, John

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 22, 2008 9:12 am

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Mon Dec 22, 2008 1:40 pm

let me take a crack at this.

stmt 1: 3r +2s = 6.
This is insufficient coz only one point (x,y) (possibly few more points coz of the <= symbol in the Q ) will lie on the straight line. This point can be found out by replacing r,s with x,y respectively and solving the simultaneous equations. 3x +2y =6 and 2x +3y <= 6.

So insufficient.

Stmt2: r <=3 and s <=2

r and s can be any value. And their combination need not satisfy the eqn for Region R.
Hence insufficient.

Combining them does not yield a single solution. coz some points can be in R and some may not be.
So E

HT Helps

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Bidisha800: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sun Sep 28, 2008 11:00 amFollowed by: 1 member; Location: USA; Thanked: 6 times

by Bidisha800 » Wed Dec 31, 2008 12:05 am

2x+3y<=6 is the line that intercepts y axis in (0,2) point and X axis at (3,0) point. All points below this line denotes the region of (x,y)

STMT 1 clearly doesn't satisfy this condition.

but as per my graph, STMT #2 satisfies this condition

Take any value of r,s where r<=3 and s <=2 and 2r+3s <=6.

Can someone explain why not (B) ?

Drill baby drill !

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Wed Dec 31, 2008 12:29 am

Bidisha800 wrote:2x+3y<=6 is the line that intercepts y axis in (0,2) point and X axis at (3,0) point. All points below this line denotes the region of (x,y)

STMT 1 clearly doesn't satisfy this condition.

but as per my graph, STMT #2 satisfies this condition

Take any value of r,s where r<=3 and s <=2 and 2r+3s <=6.

Can someone explain why not (B) ?

from the graph we can see that x have to < =3 and y < = 2
but there can be combinations like

( 3, 1 ) which would not satisfy the orginal equation...

Admission champion, Hauz khaz
011-27565856

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Wed Dec 31, 2008 12:34 am

Its great to see some GMAT focus question here. Can you share some more of them please? Or if possible all? Please comment. I am awaiting for ur resposnse.

As for as solving goes:

You need to make an XY graph and cover the appropriate region covered by the line, it will give you the clue. You may refer similar Q in OG books too.

Regards,
nagendra

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