Win_the_gmat wrote:From the consecutive integers -10 to 10, inclusive, 20 integers are randomly chosen with repetitions allowed.What is the least possible value of the product of the 20 integers?

We need to select 20 integers such that their product is lowest.
The biggest value we can obtain is 10^20 but that will be a positive number. If we can somehow make it negative, it'll be the smallest possible product. We can make it negative, if we multiply odd number of 10s and odd number of -10s. For example, one 10 and nineteen -10 or three 10 and seventeen -10 etc.

Hence, least possible product = 10*[(-10)^19] = -(10)*(10^19) = -(10^20)