Is the product of all the integers positive?

A - prdt of greatest and smallest integer is +ve
B- there is an even # of integers in the list

ans: C.
why is answer not E? i.e what is list is even and is 1, 5, -3 and 10? then A is true and so is B but prdt NOT +ve.
But if all the integers were +ve then prdt IS +ve.
hence - E.

http://www.manhattangmat.com/forums/a-certain-list-consists-of-several-different-integers-t1002.html

when you post a PROBLEM STATEMENT, please take the extra 1-2 seconds to type out words like 'product', 'several' and 'positive' in full; not only are 'prdt', '+ve', and 'sev' difficult to read, but they also make your post essentially impossible to find with the search box.

thank you.