1)
Either all the numbers in the list are positive or all the numbers in the list are negative given we take the smallest and the biggest.
Nevertheless, we cannot say if the product of all the numbers is positive or negative given that it is possible that in the case of a list of only negative number, there is an odd number of integers.

2)
Does not help us, because it is possible there are some positive and some negative numbers.

1) and 2)
We know all the numbers are either all positive or all negative.
There is an even number of integers, so in case of the list with only negative integers, the product of them is positive. In the case of only positive integers, the product of them is positive.
So C

Sorry but I dont understand the reasoning provided above...
"We know all the numbers are either all positive or all negative. "
I'm not sure how are you deriving on this

Why does list contains intergers with same sign... positive or negative
A list can be {-10,-9,6, -2}.
This also satifies the condition in 1 & 2

hence IMO E

sharad wrote:Sorry but I dont understand the reasoning provided above...
"We know all the numbers are either all positive or all negative. "
I'm not sure how are you deriving on this

Why does list contains intergers with same sign... positive or negative
A list can be {-10,-9,6, -2}.
This also satifies the condition in 1 & 2

hence IMO E

Your example does not actually satisfy statement #1.

1)The product of the greatest and smallest of the integers in the list is positive

In your example -10 x 6 = -60. As long as the greatest integer is 0 or above your set of numbers does not work.

Make sense now?

agree with you... C is correct