Does the integer K have a factor P such that 1<P<K?
please show & explain workings
The question can be rephrased as is K prime, because if K being prime is the only time that 1<P<K will not hold true.
(1) is very insufficient. It just says that K>24. Plenty of primes and non-primes out there.
(2) You gotta find out if there are any primes btwn 13!+2 and 13!+13
If you add a number to a multiple of that number, the sum will also be a multiple of the number (i.e. 4 is a multiple of 2, so 4+2 will also be a multiple of 2). Which means that the sum cannot be prime.
13! is a multiple of every # btwn 1 and 13, inclusive. Therefore, if you add any number btwn 1 and 13 to 13!, the sum will be a multple of the addend and thus will not be prime. Hence (2) is sufficient.
B is the answer.