RiyaR, please read: https://www.beatthegmat.com/read-this-fi ... tml#729339RiyaR wrote:If -1 < x < 0, which of the following must be true?
I. x 3 < x 2
II. x 5 < 1 - x
III. x 4 < x 2
I have formatted the question as follows:
USEFUL RULES:If -1 < x < 0, which of the following must be true?
I. x³ < x²
II. x� < 1 - x
III. x� < x²
(negative)^(ODD integer) = some negative value
(negative)^(EVEN integer) = some positive value
I. x³ < x²
x is NEGATIVE. So, the above rule tells us that x³ is negative, and x² is positive
So, it must be true that x³ < x²
II. x� < 1 - x
x is NEGATIVE. So, the above rule tells us that x� is negative.
Also, since x is negative, 1 - x must be positive
So, it must be true that x� < 1 - x
III. x� < x²
We can take this inequality and divide both sides by x² (since we can be certain that x² is positive).
When we do so, we get: x² < 1, and this is definitely true.
We know that x² is less than 1 because we're told that -1 < x < 0
So, it must be true that x� < x²
So all 3 statements must be true.
Cheers,
Brent
