The absolute value of a negative number can be calculated by simply removing the negative symbol. Therefore,

All four (negative) numbers in the set are less than this positive number.

Let's reductively consider what this data tells us.

Consider each group (a,b,c) as a group of signs.

From abc < 0, we know that the following are possible:

(–, +, +), (+, –, +), (+, +, –), (–, –, –)

From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)

From bc > 0, we know that we must eliminate (+, +, –)

Therefore, any of our answers must hold for (–, –, –)

This eliminates immediately a > 0, b > 0

Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.

Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.

We are left with a + b < 0, which is true, for two negatives added must be negative.