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Q59·CSAT · Prelims 2025

Real number between 0 and 1 - inequalities

NumericalNumber PropertiesNumber theoryMedium

Question

Let x be a real number between 0 and 1. Which of the following statements is/are correct? I. x² > x³ II. x > √x Select the correct answer using the code given below:

  1. 1.

    x² > x³

  2. 2.

    x > √x

Options

a

I only

Answer
b

II only

c

Both I and II

d

Neither I nor II

Explanation

The variable x is a positive fraction (0 < x < 1). Statement I: Since x < 1, multiplying both sides by a positive value yields x³ < x² (or x² > x³). This is true. For fractions, higher powers result in smaller values. Statement II: Since x < 1, taking the square root of both sides gives √(x) < 1. Multiplying both sides by √(x) gives x < √(x). Therefore, x > √(x) is false. (e.g., if x = 0.25, √(x) = 0.5, and 0.25 is not greater than 0.5).

For any real number x between 0 and 1, the hierarchy of powers is inverted: x³ < x² < x < √(x).

Answer: (a).

Question details

Year

2025

Paper

CSAT

Question

Q59

Section

Numerical Ability

Sub-topic

Number Properties

Type

Number theory

Difficulty

Medium

Source hint

Number theory

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