Real number between 0 and 1 - inequalities
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.
x² > x³
- 2.
x > √x
Options
I only
II only
Both I and II
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 x² 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).
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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