If -1 < x < 0, which of the following must be true?
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10 Mar 2021, 10:04
This is a numbers theory question. Since -1 < x < 0, it follows that x is a negative fraction (e.g., -1/3). To make things easy, pick your favorite negative fraction--mine is -1/2.
I) x < x^2: TRUE
x is always negative, x^2 is always positive. To ensure that we are correct, test with -1/2
-1/2 < 1/4
II) x^2 < x^3: FALSE
x^2 is always positive, and x^3 is always negative.
III) x < x^3: TRUE
Now, this is the tricky part, and it is the reason why I spending precious time testing a fraction. To avoid traps, test immediately:
-1/2 ? (-1/2)^3
-1/2 < -1/8
Notice that -1/8 is bigger because it is less negative and closer to zero. You can also draw the number line if you are having trouble seeing this.
My answer is D.
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