For two distinct real numbers $x$ and $y$, which of them is bigger? Statement I : $x^2

Question

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

Accepted Answer

Select this option if the question cannot be answered even using any of the statements

Explanation: Statement I alone: x² < y < 1 allows y to be anywhere between x² and 1. For x = 0.5, y = 0.3 gives x > y; for x = 0.5, y = 0.9 gives y > x. Insufficient. Statement II alone: y < √x < 1 requires x ∈ (0,1) but doesn't fix the relationship. For x = 0.25, y = 0.4 gives y > x; for x = 0.81, y = 0.1 gives x > y. Insufficient. Both together: x² < y < √x with x ∈ (0,1). Since x² < x < √x for x ∈ (0,1), y can still lie on either side of x. Examples: x = 0.25, y = 0.1 → x > y; x = 0.25, y = 0.4 → y > x. Both conditions are satisfied but the relationship remains ambiguous. Therefore, the question cannot be answered even using both statements, making Option 4 the correct answer.

Detailed Explanation:

Question 1 of 2 Data Interpretation

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