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Simultaneous Inequalities

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Manager
Joined: 18 Jun 2007
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Simultaneous Inequalities [#permalink]  26 Sep 2007, 23:14
IS XY > 0 ?

(1) x-y > -2
(2) x-2y < -6

I dont remember how to solve simultaneous inequalities .. does any one remember the procedure
Director
Joined: 03 May 2007
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Schools: University of Chicago, Wharton School
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Re: Simultaneous Inequalities [#permalink]  27 Sep 2007, 00:39
tlntd42 wrote:
IS XY > 0 ?

(1) x-y > -2
(2) x-2y < -6

I dont remember how to solve simultaneous inequalities .. does any one remember the procedure

1: x - y > -2
x + 2 > y

x and y could be anything : +ve or -ve. not suff.

2: x - 2y < -6
x + 6 < 2y

x and y could be anything : +ve or -ve. also not suff.

1 and 2: now we can say x and y both are +ves. if onl y they are +ve, then 1 and 2 are possible..
Intern
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Cleary S1 and S2 are INSUFF by themselves.

But to solve S1 and S2 we need to plot the boundary lines for the two equations on the XY-plane and determine the overlapping region to find all the points that satisfy both the inequalities.

However, for my solution I am getting (-6,0) (0,3) (-2,0) (0,2). However, a sample point in this region is not satisfying both the equations. 'IF' any point in this region satisfies both the equations, then, since x is -ive and y is positive XY <0> S1 + S2 are both required.

After going this far, if I had to guess, I would choose C.

What is the OA though?
Intern
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Ans C as weel.
If you draw the lines then the area of solutions is the the X+ Y+ quadrant.
=> XY >0
VP
Joined: 08 Jun 2005
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Is xy > 0 ?

statement 1

x-y > -2

x > y-2

insufficient

statement 2

x-2y < -6

x < 2y-6

insufficient

both statements

x > y-2 ---> from statement 1

x < 2y-6 ---> from statement 2

y-2 < 2y-6

4 < y

solve for x:

x > y-2 ---> x > 2

so x*y has to be positive.

sufficient

Director
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Neither statement is SUFF.
After solving the equation I am getting following result:

y > 4
x > 2

Hence x*y > 0 , thus C.

- Brajesh
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