KarolPL wrote:

Hello Everyone,

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.

Since each statement is sufficient, Ans D it is.

Hope it helps.

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