If x is a positive integer, is x! + (x + 1) a prime number?
(1) x < 10
(2) x is even
(1) x < 10
(2) x is even
What we think, we become
It should be E
1) We know that x < 10 and x is a positive integer. Therefore, x ranges from 1 to 9. Substitute values of x until you get 2 different answers,
x=1, 1+2=3 (YES)
x=2, 2+3=5 (YES)
x=3, 6+4=10 (NO). Stop right there!
Insufficient.
2) x is even
we know that when x=2, x! + (x+1) will be a prime.
Take x as 8, then x! + (x+1) will NOT be a prime.
Insufficient.
Combined, Insufficient again. Prime for x values 2,4,6 but not for 8.
Hence, E
