Step 1: Analyse Question StemThe question tells us that x is a positive number.
We have to evaluate if \(x^2\) < x.
Using the number line is an effective approach in solving these kind of questions.
On the number line, 4 intervals can be marked and the relationship between different functions can be easily compared.
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Of the four intervals, \(x^2\) < x is satisfied only when 0 < x < 1. Therefore, the question can be rephrased as, “ Is 0 < x < 1?”
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCEStatement 1: 0.1 < x < 0.4
This information answers the question directly and tells us that 0 < x < 1.
The data in statement 1 is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: \(x^3\) <\( x^2\)
Picking values from the 4 different intervals on the number line, we see that \(x^3\) < \(x^2\) is satisfied when x lies in the following ranges:
However, it is important to note that the question mentions that x > 0. Therefore, the first range can be ruled out and hence, the only range which satisfies the given inequality is 0 < x < 1.
The data in statement 2 is sufficient to answer the question with a definite YES.
Statement 2 alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.