Is k between 0 and 1? /700+

[Night reader]

Is k between 0 and 1?
(1) k^2 > k^3
(2) - k > k^3

[Rahul@gurome]

Is k between 0 and 1?
(1) k^2 > k^3
(2) - k > k^3

Statement 1: k² > k³
.... k³ < k²
=> (k³ - k²) < 0
=> k²(k - 1) < 0
=> (k - 1) < 0 ........... k² > 0 and certainly k ≠ 0.
=> k < 1

k may or may not be between 1 and 0.
Not sufficient.

Statement 2: -k > k³
.... k³ < -k
=> (k³ + k) < 0
=> k(k² + 1) < 0
=> k < 0 .................. (k² + 1) > 0

k is not between 1 and 0.
Sufficient.

The correct answer is B.

[Night reader]

Is k between 0 and 1?
(1) k^2 > k^3
(2) - k > k^3

Statement 1: k² > k³
.... k³ < k²
=> (k³ - k²) < 0
=> k²(k - 1) < 0
=> (k - 1) < 0 ........... k² > 0 and certainly k ≠ 0.
=> k < 1

k may or may not be between 1 and 0.
Not sufficient.

Statement 2: -k > k³
.... k³ < -k
=> (k³ + k) < 0
=> k(k² + 1) < 0
=> k < 0 .................. (k² + 1) > 0

k is not between 1 and 0.
Sufficient.

The correct answer is B.

absolutely, correct!
Rahul, for the last two months I had to completely remember math of my university entrance year. Thanks for explaining previous problem re mods. I have looked up my old math handbook, superior, no MGMAT or other comes even closer. So for different sets of mods we have critical points i.e. when the expressions (equations or inequalities) turn 0. We plot critical values on the number line and for every set solve the mods.

the rule of four zones I got from Sackman's book. I started applying it as a tool, but fundamental understanding (remembering) of all the behinds was important for me today.

[goyalsau]

=> k(k² + 1) < 0
=> k < 0 .................. (k² + 1) > 0 It shouldn't be (k² + 1) < 0