One look at the number 5040 tells us it is divisible by 10 as well as 9.
So, there is a pretty good chance 9 and 10 are two of those four consecutive integers.

Now, 5040/(9*10) = 56 = 7*8

So, the four consecutive integers are either 7, 8, 9, and 10 or -7, -8, -9, and -10.
It is evident that there cannot be any other four consecutive integers as their product would be either less than or greater than 5040.

Now, for statement 1, as j is prime, only possible value of j is 7.
So, statement 1 is sufficient.

And, for statement 2, as j is the smallest of the four, j can be either 7 or -10.
So, statement 2 is not sufficient.

Answer : A