If k is an integer, is k^3 > k?

I agree with B.

1) could be 0 or 1 ---- doesn't work
Could be 2 or greater --- works

NS - depends on values of chosen

2) could be 2, 3, 5, ... + --- works

S - K^3 must be > K

As it is given K is an integer, the only way the given eqn. ll hold true only if K is positive integer.
1) It may seem possible but remember 0 is also non-negative in which case the eqn. ll not hold true but if K is positive it will. So, two different answers not sufficient
2) K is prime - Sufficient because only positive integers are primes

(1) k is not negative [Insufficient] k could be 0 or 1, making the statement false, or an integer greater than 1, making the statement true.
(2) k is prime [Sufficient] All prime integers are positive and are greater than 1, so the value of k^3 will always be greater than k.

The correct answer is B.

Let's address the inequality.

\(k^3-k>0\) which leads to \(k^3-k=0\) --> k(\(k^2-1)=0\). We want to figure out whether x<0 ; x>1.

1) k is not negative. k can be 0, 1 or greater than one.

2) k is prime thus k>=2. Sufficient.

Answer B.
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Hi sterling19,

You've chosen the correct answer, but the reasoning that you've offered in Fact 1 is NOT correct/complete.

If K = 0, then 0^3 = 0 and the answer to the question is NO
If K = 1, then 1^3 = 1 and the answer to the question is NO

IF K > 1 though, then K^3 will be greater than K and the answer to the question would be YES.

While I'm fairly sure that you knew what you were doing and that you just mis-typed your ideas, if your goal is to score at a high-level (say, 700+), then you'll have to make a point out of being precise with your work. Most GMAT questions do not come with a "safety net" - if you make any little mistakes, then you'll get questions wrong that you shouldn't.

GMAT assassins aren't born, they're made,
Rich

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: B

Statement (1) tells us that k is either zero or a positive integer. For any positive integer value of k other than 1, k^3 > k, but if k is 1, k^3 = k, so statement (1) is insufficient. Statement (2) tells us that k is a prime number. Since all prime numbers are positive integers greater than 1 and k is prime, k^3 > k and this statement is sufficient.
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\(k^3-k >0 ?\)
\(k^2*(k-1) > 0\)
\(k^2\) will always be positive
so question boils down to Is \((k-1) > 0\)

option A: K is non negative
At K=1 Answer is NO
At K=2 Answer is Yes.

Option B : k is prime
K-1 will always be positive as smallest prime is 2
Sufficient.

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