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# Is ab > 0? (1) a b > 0. (2) a + b <0

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Is ab > 0? (1) a b > 0. (2) a + b <0 [#permalink]  15 Feb 2011, 13:09
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173. Is ab > 0?
(1) a – b > 0.
(2) a + b <0.
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Re: Is ab > 0? (1) a – b > 0. (2) a + b <0. [#permalink]  15 Feb 2011, 13:39
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banksy wrote:
173. Is ab > 0?
(1) a – b > 0.
(2) a + b <0.

Note that:
You can only add inequalities when their signs are in the same direction:

If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 3<4 and 2<5 --> 3+2<4+5.

You can only apply subtraction when their signs are in the opposite directions:

If a>b and c<d (signs in opposite direction: > and <) --> a-c>b-d (take the sign of the inequality you subtract from).
Example: 3<4 and 5>1 --> 3-5<4-1.

Back to the original question:

Is ab > 0?

Question basically asks whether a and b have the same sign.

(1) a – b > 0 --> a>b. Not sufficient to say whether a and b have the same sign.

(2) a + b <0 --> a<-b. Again not sufficient to say whether a and b have the same sign.

(1)+(2) subtract (2) from (1): (a-b)-(a+b)>0 --> b<0 --> but a could still be positive or negative (or even zero), for example: a=-1 and b=-2 or a=1 and b=-2. Not sufficient.

Or: as from (1) b<a and from (2) a<-b then b<a<-b --> a<|b| --(b)-----0-----(-b)-- --> a is somewhere between b and {-b} so it can be positive, negative or zero). Not sufficient.

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Re: Is ab > 0? (1) a – b > 0. (2) a + b <0. [#permalink]  16 Feb 2011, 13:14
same trick as the other one you posted. good luck. thanks for posting.
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Re: Is ab > 0? (1) a – b > 0. (2) a + b <0. [#permalink]  17 Feb 2011, 23:52
banksy wrote:
173. Is ab > 0?
(1) a – b > 0.
(2) a + b <0.

Try picking numbers and applying them considering different possible scenarios.

(1) a-b > 0
Case 1. a= -2 b= -5
a-b=-2-(-5)= 3. Condition satified.
So is ab>0? Yes.

Case 2. A= 5, B=(-3)
a-b= 5-(-3)= 8. Condition satisfied.
So is ab>0? No.

2 different answers. Hence this statement is insufficient.

(2) a+b<0

Case 1. a=- -10 , b= -5.
a+b=(-10-5)=-15. Condition Satisfied.
So is ab>0? Yes.

Case 2. a= -10 , b= 5
a+b= (-10+5)=-5. Condition satisfied.
So is ab>0?. No.

Again, 2 different answers. Hence this statement is also not sufficient.

1&2 Combined: Not sufficient as we can pick any combination of positive/ negative numbers.

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Re: Is ab > 0? (1) a – b > 0. (2) a + b <0.   [#permalink] 17 Feb 2011, 23:52
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