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Q62·CSAT · Prelims 2026

Data Sufficiency — Real Number Properties

DI / DSData SufficiencyData Sufficiency● Medium

Question

Question : For two distinct real numbers x and y, which of them is bigger? Statement I : x^2<y<1 Statement II : y<√(x)<1

Options

a

Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

b

Select this option if the question can be answered using either statement alone

Answer
c

Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

d

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

Explanation

The problem asks us to determine the relative size ordering between two distinct real numbers x and y .

Analyze Statement I: x² < y < 1.
Since y < 1, both numbers are bounded. Let us test fractions: if x = 0.5, then x² = 0.25. A valid y could be 0.4, which gives 0.25 < 0.4 < 1. Here, y > x (0.4 > 0.5 is false, so x > y).
What if x = -0.5? Then x² = 0.25. A valid y could be 0.4, giving 0.25 < 0.4 < 1. Here, y > x (0.4 > -0.5). Since x can be positive or negative, changing the relative order, Statement I is not sufficient alone .
Analyze Statement II: y < √(x) < 1 .
For √(x) to be real and less than 1, x must be a positive fraction (0 < x < 1).
In the domain of positive fractions, we know that x < √(x) (e.g., 0.25 < √(0.25) = 0.5).
The statement gives y < √(x). This doesn't strictly lock the position of y relative to x, as y can be smaller or larger than x while remaining below √(x). For example, if x = 0.25 \rightarrow √(x) = 0.5. y could be 0.1 (y < x) or 0.4 (y > x). Thus, Statement II is not sufficient alone.
Combining both statements: x² < y < √(x) < 1. In the positive fractional domain, x² < y < √(x) still allows y to shift around x, leaving the exact order uncertain.
For data sufficiency questions involving fraction inequalities, testing points across both negative and positive fractional domains help determine if an order is unique.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Q62

Section

Data Interpretation

Sub-topic

Data Sufficiency

Type

Data Sufficiency

Difficulty

Medium

Source hint

Inequalities — fractional and roots interval logic

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