abhi758 wrote:Is X negative?
1. x^3(1-x^2)<0
2. x^2-1<0
Please explain your answer..
Ron, how do I go about applying your strategy of picking numbers combining both statements to check for option C or E right in the begining? Am looking for a 2 min solution here. Look forward to your reply.
C
There are two parts of the equation that are important to watch out for.
(x^3) always takes on the sign of X
(1-x^2) depends on how large X is. If x^2 is >1, it is positive, if x^2 is smaller than 1 it becomes negative.
note that X cannot be 0
pick:
-------- (x^3)*(1-x^2)-------
x=2: (Pos)*(neg) = neg
x=0.5: (Pos)*(pos) = pos
x=-0.5: (neg)*(pos) = neg
x=-2: (neg)*(neg) = pos
So, with both x=2 and x=-2 the equation holds, but you can't say whether X is negative, it could be both. => insufficient
Statement 2: restricts the value of X: x^2-1<0 => x^2<1, so this holds
1>X>-1 (because for any X larger than 1 or smaller than -1, the statement wouldn't hold). So X doesn't have to be negative. => insufficient
Together:
so: since
1>X>-1, it follows that (1-x^2) will always be positive!
Therefore X^3 must be negative for statement 1 to hold, which must X is negative!
Therefore, together the statements are sufficient
