singhsa wrote:If x < 0 and 4 < 5 - xy < 5, which of the following must be true?

I y < 0
II xy < 1

In this question, the answer is
I and II

But, from the equation, we get that 0<xy<1. Thus xy must be between 0 and 1. If xy= -20, the statement would not be valid. So, how can we consider statement II from the question to be true?

If 0 < xy < 1, then it is certainly true that xy < 1; that's what the right-hand portion of the inequality 0 < xy < 1 says. If 0 < xy < 1, then it is impossible for xy to be equal to -20, so your example is not germane here. Note that you are not asked here to find an answer which is equivalent to the inequalities in the question. You are only asked to find one which must be true. If we had a third item which read, for example:

III) xy > -9

that would also be true here; we know that xy is between 0 and 1, so it's certainly bigger than -9.

Further, if we know that x is negative and that xy is positive, then y is certainly negative, so I must be true.