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b could be bigger than c and still ab < ac when b is negative but then the expression will not be bigger than 0. If "a" alone is negative also the whole expression will not be bigger than 0.

If a is negative and b is negative then ab will not be < ac.

I don't quite get a problem. I've got an inequality:

0 < ab < ac

(1) -> c < 0 -> this one I understand well (2) -> b > c

Is "a" negative?

I know that ab and ac > 0, ab < ac

b could be bigger than c and still ab < ac when b is negative but then the expression will not be bigger than 0. If "a" alone is negative also the whole expression will not be bigger than 0.

If a is negative and b is negative then ab will not be < ac.

I don't quite get it. Pls help

We are given 0<ab<ac => ab and ac both are positive.

Statement 1: c <0 => for ac to be positive , a must be negative. Sufficient

Statement 2: b >c Now lets take a look at what is given in question 0<ab<ac => ab <ac => ab-ac <0 => a(b-c) <0

But from statement 2 we know b>c thus b-c must be positive. Therefore for a(b-c) <0 to be true, a must be negative. Sufficient.

Am I on right path here? Statement 1 is fine but for statement 2 we have ac > ab > 0 and b > c I want to plug in values and solve this one.

let b = 5 and c = 3 , so b > c is satisfied . this will mean 3a > 5 a > 0 , so a needs to be positive for this to be greater than zero but 3a can never be greater than 5a , if a is positive so we cannot consider this.

b = -3 , c = -5 ac >ab>0 means -5a > -3a > 0 which will hold when a < 0 . So statement 2 is sufficient as well.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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(D): By the transitive property of inequalities, if 0 < ab < ac, then 0 < ac. Therefore, a and c must have the same sign.

(1) SUFFICIENT: Statement (1) tells you that c is negative. Therefore, a is negative.

(2) SUFFICIENT: Statement (2) is trickier. The statement indicates that b > c, but the question stem also told you that ab < ac. When you multiply both sides of b > c by a, the sign gets flipped. For inequalities, what circumstance needs to be true in order to flip the sign when you multiply by something? You multiply by a negative. Therefore, a must be negative, because multiplying the two sides of the equation by a results in a flipped inequality sign.

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