Question

If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?

Answer 1

First, since it makes the negative a positive, b must be negative.

Then, since the end result is less than a, we can write
ab < |a|

From this, we get two equations

1. ab2. ab>-a

1.
abb<1

2.
ab>-a
b>-1

So, b is in-between -1 and 1, but since we’ve determined that is negative, -1