Hi shibsriz,
I'm a big fan of Number Properties and patterns (since both appear on the GMAT repeatedly). However, you DO NOT have time to stare at the screen, trying to figure out IF there's a pattern to be found. As such, sometimes you have to "jump in" and TEST VALUES.
This DS prompt gives us a lot of info to work with. We're told that K is a POSITIVE INTEGER. We're asked if it's prime. This is a Yes/No question.
Fact 1: K is NOT divisible by anything from 2 to (rootK), inclusive.
Since K is NOT divisible by 2, that means that K CANNOT be EVEN.
We CANNOT use K = 1, since root1 divides into 1.
If K = 3, nothing from 2 to root3 divides evenly into 3, so 3 IS allowed. The answer to the question is YES
If K = 5, nothing from 2 to root5 divides evenly into 5, so 5 IS allowed. The answer to the question is YES
We CANNOT use K = 9, since root9 = 3 and 3 divides into 9.
We CANNOT use K = 15, since 3 divides into 15 (and 3 is between 2 and root15).
It appears that the only numbers that "fit" Fact 1 are PRIMES. This is consistent.
Fact 1 is SUFFICIENT
Fact 2: K is NOT divisible by anything from 2 to K/2, inclusive AND K > 5
Since K is NOT divisible by 2, that means that K CANNOT be EVEN
If K = 7, nothing from 2 to 7/2 divides into 7, so 7 IS allowed. The answer to the question is YES
We CANNOT use K = 9, since 3 divides into 9 (and 3 is between 2 and 9/2).
If K = 11, nothing from 2 to 11/2 divides into 11, so 11 IS allowed. The answer to the question is YES
We CANNOT use K = 15, since 3 divides into 15 (and 3 is between 2 and 15/2).
It appears that we have a similar pattern here; the only numbers that "fit" Fact 2 are PRIMES. This is consistent.
Fact 2 is SUFFICIENT.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
