lets simplfy the question first..
is k a prime number,
statement 1 : k>4! not suff
statement 2 : 13! + 2 <= k <= 13! + 13
2 is factor of 13!, so 2 is for 13!+2 also
3 is factor of 13!, so 3 is for 13!+3 also
4 is factor of 13!, so 4 is for 13!+4 also
similarly you can go upto 13 ....
means k is not a prime number. suff
ds4
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Source: Beat The GMAT — Data Sufficiency |

















