Civil Services Prep

Prelims 2026 · CSAT / Quantitative Aptitude · Question 2

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

  1. Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
  2. Select this option if the question can be answered using either statement alone
  3. Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
  4. Select this option if the question cannot be answered even using any of the statements

Answer

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

Statement I: x^2 < y < 1. Example x=0.5, y=0.3 gives x>y; but x=0.5, y=0.8 gives y>x. Not sufficient.
Statement II: y < √x < 1. Example x=0.25, y=0.1 gives x>y; but x=0.25, y=0.4 gives y>x. Not sufficient.
Together: x^2 < y < √x < 1 with 0<x<1. Since for 0<x<1, we have x^2 < x < √x, y can still lie on either side of x. So even together, comparison is not fixed.

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