83. Is x3 greater than x ?
(1) x + x3 > 0
(2) x - x3 < 0
x3(denoting x cube in the above question)
The Answer to the above data sufficiency question is provided as (b)
But I am arriving at a different answer
(a)A is definitely not correct since there could be a scenario where a is an integer say for eg 3 which makes x3 =27 greater than zero
x could also be a positive fraction so essentially there could be two cases where for (1)x 3 > x and second x3 is less than x
(2)B in my view also appears incorrect since the text fails to consider the possibility of a fraction where x can be greater than x3 say assuming x is -1/2
X could also be a positive integer making x3 greater than 3 (Assume x =3)
Please resolve what should be the appropriate answer to the question and whether b is actually the correct option
Actually statement 2 gives you the answer directly.
Question: Is \(x^3 > x\)?
(2) \(x - x^3 < 0\)
\(x < x^3\)
This gives you straight away that x^3 is greater than x. So you answer with a definite 'Yes'.
Statement 2 alone is sufficient.
You are correct about statement 1.
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