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# No. Properties

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Senior Manager
Joined: 05 Oct 2008
Posts: 263
No. Properties [#permalink]

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27 Jan 2009, 09:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

is xy > 0?

x - y > -2
x - 2y < -6
Manager
Joined: 04 Jan 2009
Posts: 235
Re: No. Properties [#permalink]

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27 Jan 2009, 09:50
study wrote:
is xy > 0?

x - y > -2
x - 2y < -6

both are required. let us check if they are suff:
x-y>-2
-x+2y>6
y>4 and x>-2+y>-2+4>2
both together sufficient.
_________________

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tusharvk

SVP
Joined: 17 Jun 2008
Posts: 1504
Re: No. Properties [#permalink]

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27 Jan 2009, 11:31
In the simplest form,

For stmt1: assume that y = 0, then x > -2 and xy = 0.

Similarly, for stmt2: if y = 0 then xy = 0.

Combining both,
-2 < x-y < y-6
or, y > 4
and hence x > 2 and accordingly, xy > 0.

Hence, C.
Current Student
Joined: 28 Dec 2004
Posts: 3312
Location: New York City
Schools: Wharton'11 HBS'12
Re: No. Properties [#permalink]

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27 Jan 2009, 15:11
I get E for some reason...

i am drawing this as a line

1)y<X+2 which is linear line and y is the region where below the line..in that case you can have where x, y>0 or x, y<0 or x<0 y>0 in this case xy<0

2) same thing y>x/2 + 3 y>0 as long as -x/2<3 however if -x/2<3 then y<0 and thus xy>0 but there is a region where y>0 and x<0 and thus xy<0

together too the posibility exists that x<0 and y>0
Manager
Joined: 04 Jan 2009
Posts: 235
Re: No. Properties [#permalink]

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27 Jan 2009, 15:30
fresinha12 wrote:
I get E for some reason...

i am drawing this as a line

1)y<X+2 which is linear line and y is the region where below the line..in that case you can have where x, y>0 or x, y<0 or x<0 y>0 in this case xy<0

2) same thing y>x/2 + 3 y>0 as long as -x/2<3 however if -x/2<3 then y<0 and thus xy>0 but there is a region where y>0 and x<0 and thus xy<0

together too the posibility exists that x<0 and y>0

Even if you draw these two lines you get the same result. I drew the lines y<x+2 (slope 1 and y intercept=2) y is below that line.
Then y>x/2+3. slope=1/2 and y intercept = 3. Y lies above this line. Thus x and y are to the right of the intersection point defined by the two lines viz. (2.4).
Hence, xy>0
_________________

-----------------------
tusharvk

Re: No. Properties   [#permalink] 27 Jan 2009, 15:30
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# No. Properties

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