davidforsberg wrote:x<0???
1) (x^3)(1-x^2) < 0
2) x^2<1
answer is C. Anyone care to elaborate?
To elaborate on It'sme's solution (btw, if you disable HTML, the formatting issues will go away):
(1) if the product of two terms is negative, then exactly one of those terms must be negative. So, either:
(x^3) < 0
(therefore x < 0)
or
(1 - x^2) < 0
(therefore 1 < x^2)
We can pick numbers to make x positive or negative, so (1) is insufficient.
(2) x^2 < 1
To make this true, -1 < x < 1 (i.e. x is a fraction or 0). So, x could be positive, negative or 0: insufficient.
If we combine the statements, we know that:
x^2 < 1
AND
x^3 < 0
In other words, we've eliminated the "1 < x^2" possibility from statement (1), since it conflicts with statement (2).
If we know for sure that x^3 < 0, then x MUST be < 0. Therefore, together the statements are sufficient: choose (c).
