DS Divisibility Question

[payal919]

Q: If x is a positive integer, is x! + (x + 1) a prime number?
(1) x < 10

(2) x is even

Answer provided by MGMAT for (2) being insufficient

(2) INSUFFICIENT: Statement (2) says that x is even, so let's again consider x = 2:
2! + (2 + 1) = 5, which is prime.

Now consider x = 8:
8! + (8 + 1) = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) + 9.
This expression must be divisible by 3, since both of its terms are divisible by 3. Therefore, it is not a prime number.

Can you please explain what MGMAT is trying to say regarding the explanation for x=8, i am not sure what it means by both of its terms?

Also is there a faster way to solve (2) if x=8?
This is where I got stuck, where I didn't know if I should do the tedious calculation for 8! I feel like there has to be an alternative way to solve this.

[tim]

the two terms we are referring to are 8! and 9. you definitely don't have to do the tedious calculation of 8x7x6x5x4x3x2x1; as long as you recognize that it has a 3 in it as a factor somewhere that's enough to know that 8! is divisible by 3. since 9 is also divisible by 3, so is their sum..