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There is a trick in question. the q. says "X/|X| < X" is always true (!).
it is possible only if x is of (-1,0)&(1,+∞). therefore we should find condition that covers all range.
x > 1 is not include (-1,0) - is inappropriate. x > -1 - is appropriate, covers all range. |X| < 1 is not include (1,+∞) - is inappropriate. |X| = 1 is not include all range (-1,0)&(1,+∞) - is inappropriate. |X|^2 > 1 is not include (-1,0) - is inappropriate.