Solution
To find:Analysing Statement 1• As per the information given in statement 1, \(x^3 < x\)
Simplifying, \(x^3 – x < 0\)
Or, \(x (x^2 – 1) < 0\)
Or, \(x (x – 1) (x + 1) < 0\)
• This is true when 0 < x < 1 or x < -1
Since x can be both positive or negative, we cannot say whether x > 0 or not
Hence, statement 1 is not sufficient to answer
Analysing Statement 2• As per the information given in statement 2, x is even
• The value of x, being even, can be both positive and negative
Hence, statement 2 is not sufficient to answer
Combining Both StatementsIf we combine the information present in both the statements, we can say
• The value of x lies in the range x < -1 as there are no even integers possible in 0 < x < 1.
Therefore, we can say x is not greater than 0
Hence, the correct answer is option C.
Answer: CIn the equation (x-1)(x)(x+1)<O, (x-1) < 0 => x<1; (x+1)<0 => x<-1, then shouldn't x<0 be also considered?
You've concluded that 0<x<1. Couldn't understand that part.