GIVEN: a and b are integers, and ab = -5
Using integers, there are only four ways to get a product of -5:
case a: a = 1 and b = -5
case b: a = -1 and b = 5
case c: a = 5 and b = -1
case d: a = -5 and b = 1

HOWEVER, we're also told that a − b > 0
If we add b to both sides of that inequality, we see that a > b
If a must be greater than b, then we can rule out case b and case d.

This leaves us with only two possible cases:
case a: a = 1 and b = -5
case c: a = 5 and b = -1

Now check the statements:
I. a > -1
Since cases a and c BOTH confirm that a > -1, statement I MUST be true

II. b is odd
Since cases a and c BOTH confirm that b is odd, statement II MUST be true

III. |a| = 5
In case a, |a| = |1| = 1. So, statement III NEED NOT be true

Answer:

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