Is K a positive number?
(1) |K^3|+1>K
(2) K+1>|K^3|
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Both statements are satisfied if k=0 or if k=1.
If k=0, then K is not positive.
If k=1, then K is positive.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is E.
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A useful observation here: the first statement is true of ANY number. So S1 is totally useless, meaning the answer is either B or E.
The second statement has two cases.
Case I: k is nonnegative.
This gives us k + 1 > k³, or 1 > k³ - k, or 1 > k(k+1)(k-1). This is true if k = 0 or k+1 = 0 (among other possibilities), so S2 is INSUFFICIENT.
Just for fun, the second case gives us
Case II: k is negative, or k+1 > -k³, which obviously has a few solutions itself.
The second statement has two cases.
Case I: k is nonnegative.
This gives us k + 1 > k³, or 1 > k³ - k, or 1 > k(k+1)(k-1). This is true if k = 0 or k+1 = 0 (among other possibilities), so S2 is INSUFFICIENT.
Just for fun, the second case gives us
Case II: k is negative, or k+1 > -k³, which obviously has a few solutions itself.
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Solution :
Question : Is K > 0 ?
Statement 1) |K^3|+1>K
i.e. |K^3|+1>K
i.e. +K^3 + 1 > K
i.e. +K^3 + 1 > K OR i.e. -K^3 + 1 > K
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT
Statement 2) K+1>|K^3|
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT
Combining the two statements
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT
Answer: Option E
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