m_blooms wrote:Does the integer k have a factor p such that 1<p<k
(1) "k>4!"
(2) "13!+2 <= k <= 13!+13"
I know its asking something about prime numbers...HELP PLEASE?
The question is really asking "is k prime?"
If k is prime, then there will be no factor of k between 1 and k.
If k is not prime, then there will be a factor of k between 1 and k.
The only exception is that if k is less than or equal to 1, of course there will be no factors between 1 and k.
(1) k > 4
Well, there are lots of primes and non-primes greater than 4: insufficient.
(2) 13! + 2 <= k <= 13! + 13
There will be no primes in this range, so this statement is sufficient.
Here's how we know:
Every number from 1 to 13 is a factor of 13!.
Since 2 is a factor of 13!, 2 will also be a factor of 13! + 2
Since 3 is a factor of 13!, 3 will also be a factor of 13! + 3
Since 4 is a factor of 13!, 4 will also be a factor of 13! + 4
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Since 13 is a factor of 13!, 13 will also be a factor of 13! + 13
(2) is sufficient and (1) isn't: choose (b).
