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Inequalities

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Senior Manager
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Inequalities [#permalink] New post 09 Dec 2006, 04:28
Is xy>0

(1) x-y>-2

(2) x-2y<-6

Please show computations. Thanks!
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 [#permalink] New post 09 Dec 2006, 05:03
answer is C.

each statement alone is not sufficient, i think that's clear enough because this is one linear equation with two variables - not a big of a constraint. for example, take x=4 y=1 or y=-1, both satisfy statement 1, but give different answers to the question.

however, both statement are sufficient. there are several ways to get there, here is one:
x-y>-2 and x-2y<-6. if x-y>-2 and you take y out (to get x-2y) and get a number less than -6 it must be that y>4. (you could solve the equations, but i prefer not to).
now, if y>4 then from x-y>-2 => x>y-2 => x>2
so both x and y are positive ance xy>0

b.t.w to solve the equation youo should rewrite statement 2:
x-2y<-6 => 2y-x>6.
then add the two statements to get y>4.

hope it helped.

amit.
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 [#permalink] New post 09 Dec 2006, 05:36
Ditto here - solve the two inequalities to get the answer, no one alone is sufficient - C indeed
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Re: Inequalities [#permalink] New post 09 Dec 2006, 05:49
Hermione wrote:
Is xy>0

(1) x-y>-2

(2) x-2y<-6

Please show computations. Thanks!



From (1) we cannot know anything

Rewrite (2) as
x-y<y-6

which is x-y > 6-y ---(3)

Subtract (1) from (3)

you get 0 > 8-y which is

y>8

Subtsitue in 1 and plug in values you get x minium as 7

So x*y is +ve

C stands
Re: Inequalities   [#permalink] 09 Dec 2006, 05:49
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