Product will be positive only if all the numbers are positive or there is an even number of negative numbers.

1. minmum & maximum have positive product: means either both are negative or both are positive.
it means that all the numbers in the list have the same sign (either all positive or all negative)
However this is insufficient (because all negatives with odd quantity can cause problems)

2. Even number of integers does not help if there is an uneven number of negatives in the list (if it were a mix of positive/negatives).
INSUFFICIENT.

However, both of these together should suffice.

Hence C is the answer.

Let me know in case of doubts/errors, if any.

Regards,
Bharat.