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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
$$For\ x=1,\ x!\ =1\ and$$ $$x!+x+1=1+1+1=3\left(prime\ number\right)$$
$$For\ x>1,\ x!\ will\ always\ be\ even$$
Statement 1= x<10
if x=2 Therefore 2!+3 =5 (prime number)
if x=3 Therefore 3!+4=10 (even number) Hence statement 1 is not sufficient.
Statement 2 =
if x=2! Therefore 2!+3=5(prime number)
if x=14 14!+15=120 (even number)
Hence statement 2 is not sufficient
statement 1 and 2 together
= x is an even number <10
but if x=8 =8!+9=45(odd number)
both statement together are not sufficient option E because both staement together are not sufficient
