Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

algebra

hi guys, could you please help with this problem?

Is xy>0?

1) x-y>-2

2) x-2y<-6

Choose among the 5 possibilities:
A) STATEMENT 1 ALONE IS SUFFICIENT
B) STATEMENT 2 ALONE IS SUFFICIENT
C) THE 2 STATEMENTS TOGETHER ARE SUFFICIENT
D) EACH STATEMENT ALONE IS SUFFICIENT
E) THE 2 STATEMENTS TOGETHER ARE NOT SUFFICIENT

The textbook I'm practicing on gives C) as the answer, but I cannot figure it out. Could you please explain the right solving sequence?
thank you

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,423

Re: algebra

Assumption 1:- Statement 1 alone is sufficient.
That is x-y>-2. Let x=1 and y=-1. x-y=2 and x-y>-2 is true. However, xy is -1 and xy is not greater than 0.
Assumption 2: Statement 2 alone is sufficient.
That is x-2y<-6. Let x=-2 and y=5. x-2y=-2-10=-12.
x-2y<-6 is true, however, xy=-10 and xy is not greater than zero.

Assumption 3: Both statements 1 and 2 together are sufficient.
The hypothetical values taken in the first and second illustrations would not satisfy both the inequalities. We reach a conclusion, xy>0 by putting values of x and y such that the two inequalities are satisfied.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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simone

Member

Registered: 2007-10-05

Posts: 19

Re: algebra

thank you, but I don't understand the reasoning behind your last point.