Question

CSATHardPrelims 2026Maths

For two distinct real numbers $x$ and $y$ , which of them is bigger? Statement I : $x^2 < y < 1$ Statement II : $y < \sqrt{x} < 1$

Explanation

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.

Insufficient.

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

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

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.

Maths PYQs from 2026

Candidate	Score in component 1	Score in component 2	Score in component 3
1	5	4	6
2	4	6	5
3	3	2	8
4	9	4	3
5	8	8	2

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