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Is ab > 0?

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Joined: 10 Feb 2011
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Is ab > 0?  [#permalink]

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New post 15 Feb 2011, 13:09
2
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (01:22) correct 42% (00:44) wrong based on 124 sessions

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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]

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New post 15 Feb 2011, 13:39
3
2
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.

Answer: E.
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Re: Is ab > 0? (1) a – b > 0. (2) a + b <0.  [#permalink]

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New post 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.

Hence, the answer is E.
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Re: Is ab > 0?  [#permalink]

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New post 13 Mar 2016, 07:44
The basic rule => If any linear algebraic equation contains one algebraic symbol => we can alter that
so there is no way we convert the + sign or the - sign to the * sign
hence E
Also B must be always negative (from combining the inequalities)
and A>0 or A<0 so AB>0 or AB<O
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Re: Is ab > 0?  [#permalink]

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New post 22 Apr 2017, 09:28
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Re: Is ab > 0? &nbs [#permalink] 22 Apr 2017, 09:28
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