My workings:-

1>1-ab>0
1-1>1-ab-1>0-1
0>-ab>-1

One must be aware that, If all the terms in an inequality are multiplied by a negative number, the inequality reverses.(Read here - https://www.mathsisfun.com/algebra/inequ ... lving.html). For example, 5>4. but when you multiply both sides with -1, you get -5 < -4. (Did you see how the inequality reversed from > to <)

You are absolutely correct in what you did.Starting from where you left, let me multiply all the terms in the inequation with -1.
0>-ab>-1
0*1 < -1*-ab < -1*-1
0<ab<1.
So, from the equation we know that ab<1 (Option III is a MUST BE TRUE condition) and ab>0.

If the value of ab>0, a and b can be both positive(positive*positive = positive) or both negative(negative*negative = positive).
If a,b are both positive(say 1 and 2), a/b > 0 (1/2>0)
If a,b are both negative(say -2 and -2), a/b > 0 (-2/-1 = 2/1 >0)
So, the value of a/b is always greater than 0, i.e a/b > 0(so is the value of b/a). So, Option I is a MUST BE TRUE condition, if 0<ab<1.

We also know that the value of a/b can be greater than 1(=2 if a = -2 and b = -1) or less then 1(=1/2 if a = 1 and b = 2). So, condition II is not always true.

Answer E

p.s: Here is a link - https://www.beatthegmat.com/new-spoilers-t5302.html that will help you with the usage of spoilers.