Answer: The question cannot be answered even using both statements together.

Statement I alone: $x^2 < y < 1$

This gives $-1 < x < 1$ and $y < 1$, but doesn't pin down which is bigger.

• $x = 0.5,\ y = 0.3$: satisfies $0.25 < 0.3 < 1$ → $x > y$
• $x = 0.5,\ y = 0.9$: satisfies $0.25 < 0.9 < 1$ → $y > x$

Insufficient.

Statement II alone: $y < \sqrt{x} < 1$

This gives $0 \le x < 1$ and $y < 1$, again ambiguous.

• $x = 0.25,\ y = 0.4$: $0.4 < 0.5 < 1$ ✓ → $y > x$
• $x = 0.81,\ y = 0.1$: $0.1 < 0.9 < 1$ ✓ → $x > y$

Insufficient.

Both together: $x^2 < y < \sqrt{x}$, with $x \in (0, 1)$.

Note that for $x \in (0,1)$, $x^2 < x < \sqrt{x}$, so $y$ can lie on either side of $x$.

• $x = 0.25,\ y = 0.1$: $x^2 = 0.0625 < 0.1 < 1$ ✓ and $0.1 < \sqrt{x} = 0.5 < 1$ ✓ → $x > y$
• $x = 0.25,\ y = 0.4$: $0.0625 < 0.4 < 1$ ✓ and $0.4 < 0.5 < 1$ ✓ → $y > x$

Both statements together still fail to determine which is bigger.