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What is the largest number of the following statements that can be true at the same time?

I) $0 < x^2 < 1$

II) $x^2 > 1$

III) $-1 < x < 0$

IV) $ 0 < x < 1$

V) $0 < x - x^2 < 1$

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.*