komati_anusha wrote:If k is a positive integer, is 2� - 1 a prime number?
(1) k is a prime number.
(2) k has exactly two positive divisors.
While plugging in values 2 and 3 as prime numbers for k for Option A, I concluded as Sufficient, so D.
Brent, How can I pluggin right numbers like 11. What to do not to repeat the same mistake.
Thanks.
If you really wanted to answer this one, your best bet in a case in which your first two picked numbers give the same answer is to keep going up the line and look for a different answer or some kind of pattern.
If k = 2, 2� - 1 = 4 - 1 = 3. Prime
If k = 3, 2� - 1 = 8 - 1 = 7. Prime
So we keep going from a power of 2 to an odd number that is prime. So what you need to consider is this question. Is it possible that there will be a prime power of 2 that is 1 greater than a non prime number?
Given that there are infinite prime powers of 2, it seems likely that the answer to that question is "Yes."
So, while as Brent said this question may be out of scope, maybe the key takeaway for you is that in picking numbers you need to consider what is going on in the situation.
In this case, picking just the first two prime numbers is probably not going to work, as in going up the line you are likely to get a non prime result from 2� - 1.
Generally speaking, when picking numbers to plug in you need to be either getting some kind of representative sample or generating a pattern.
Since there are infinite prime powers of 2, the first two prime powers are not really a representative sample, and maybe shooting for a representative sample does not even make sense. Maybe what you really needed to do was to use plugged in numbers to find a pattern that you could then use to get to the answer.
