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If K is an Integer , Is K^3 > K?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Mar 19, 2013 2:36 pm
guerrero wrote:If K is an Integer , Is K^3 > K?

a)K is Not negative

b)K is prime

thanks !
Keep in mind that there are only 2 scenarios in which k^3 > k:
Scenario #1: k > 1
Scenario #2: -1 < k < 0

Target question: Is K^3 > K?

Statement 1: K is Not negative
There are many values of K that meet this condition. Here are two:
Case a: K = 2, in which case K^3 is greater than K
Case b: K = 1, in which case K^3 is not greater than K
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: K is prime
Since a prime number is a positive integer that has exactly 2 different positive divisors, we know that K = 2 or 3 or 5 or 7 or 11 or . . .
All of these values are greater than 1, which means K^3 is definitely greater than K
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by GMATGuruNY » Tue Mar 19, 2013 3:44 pm
guerrero wrote:If K is an Integer , Is K^3 > K?

a)K is Not negative

b)K is prime

thanks !
Since both statements indicate that k is not negative, k³>k can be true here ONLY IF K IS POSITIVE.
Thus, we can simplify the question stem by dividing each side by k and taking the square root of both sides:
k³/k > k/k
k² > 1
k>1.

Question rephrased: If k is an integer, is k>1?

Statement 1: k is not negative
Since it's possible that k=0 or k=2, INSUFFICIENT.

Statement 2: k is prime
Since every prime number is greater than 1, SUFFICIENT.

The correct answer is B.
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