Data Sufficiency

Having trouble with this one:

Is the product of four consecutive even integers positive?
1. The sum of these integers is positive but smaller than 20
2. The product of the smallest two of these integers is positive

the answer may be incorrect on the app

Is the product of four consecutive even integers positive?
Let the four consecutive even integers be 2n-2, 2n , 2n+2, 2n+4, where n is an integer.

1. The sum of these integers is positive but smaller than 20

Sun of these integers = 2n- 2 + 2n + 2n+2 + 2n+4 = 8n+4.
0<8n+4<20
-4<8n<16.
-1/2<n<2. Since, n is an integer, it can be 0 or 1.
If n = 0, the integer set is -2,0,2,4. The product of the members of the set is 0.
If n = 1, the integer set is 0,2,4,6. The product of the members of the set is 0.
For both the cases, product of four consecutive even integers is NOT positive. So, Statement I is sufficient to answer the question.

2. The product of the smallest two of these integers is positive

Case 1: If the set is -4,-2,0,2, then the product of these integers is 0.
Case 2: If the set is 2,4,6,8, then the product of these integers is greater than 0.
Since we don't have a definite answer, Statement II is Insufficient to answer the question.

IMO A

Do you also know that the product of four consecutive integers is either zero or positive.

Case 1: 1,2,3,4 - The product is Positive.
Case 2: 0,1,2,3 - The product is 0.
Case 3: -3,-2,-1,0 - The product is 0.
Case 3: -4,-3,-2,-1 - The product is Positive.

Do you also know that the product of four consecutive even integers is either zero or positive.

Case 1: 2,4,6,8 - The product is Positive.
Case 2: 0,2,4,6 - The product is 0.
Case 3: -6,-4,-2,0 - The product is 0.
Case 3: -8,-6,-4,-2 - The product is Positive.