Given n>5 , when (n!+n+1) is divided by (n+1) , what is the remainder ?
(1) (n+2) is a prime number.
(2) (n−2) is a prime number.
OAD
(1) (n+2) is a prime number.
(2) (n−2) is a prime number.
OAD
if we simplify (n!+n+1)/(n+1)
we need to find remainder of this term n!/(n+1) coz remainder of (n+1)/(n+1) is 0.
as n>5,
a. n+2 is prime --> n is definitely odd
n!/n+1 will have remainder 0. (n=9,11,15..)
Sufficient
b. n-2 is prime --> n is again definitely odd
n!/n+1 will have remainder 0. (n=7,9,13..)
Sufficient
hence D
