Hi All,

We can also solve this question using the

Wavy Line method.

Given:We are asked if \(0< x <1\). For finding the range of \(x\), we need to solve the inequality given in the statements.

Statement-I:St-I tells us that \(x^2 < x\) i.e. \(x(x -1) < 0\). Let's find the range of this inequality using the Wavy Line method.

The zero points of this inequality are {1,0}.

Plotting them on the number line using the Wavy Line method we see that the inequality is negative for the range \(0 < x < 1\).

Hence, statement-I is sufficient to answer the question.

Statement-II:St-II tells us that \(x^3 > 0\). Let's draw a Wavy line for this inequality. The zero point of the inequality is {0}

Plotting it on the number line we see that the inequality is positive for the range \(x > 0\). Thus, we can't say for sure if \(0 < x < 1\).

Hence, statement-II is not sufficient to answer the question.

For more reading on the Wavy Line method try out inequalities-trick-91482-80.html#p1465609Hope its clear!

Regards

Harsh

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