ZArslan wrote:

24. Set S consists of more than two integers. Are all the numbers in set S negative?

(1) The product of any three integers in the list is negative

(2) The product of the smallest and largest integers in the list is a prime number.

So Set S can have three or more integers.

(1) Product of any three integers is negative. Now if set S has only three integers, then the product of 'any three integers' means product of these three integers only. And if product of these three integers is negative, it could mean

either that all three are negative Or

only one of them is negative. So this is giving us two different possibilities, and so Insufficient.

If instead set has more than three integers (say four or five or hundred whatever), then for product of 'any three integers' to be negative it would only be possible if

ALL the integers in set are negative.

So from this statement, we get that if set S has exactly three integers - then either all are negative or only one is negative. But if set S has more than three integers, then all must be negative.

Not Sufficient.

(2) Prime numbers are always positive. So if we arrange the integers of set S in say ascending order, the product of smallest (first integer) and largest (last integer) is coming out to be positive. This can happen if both smallest and largest integers are negative (

in which case all integers will be negative) Or if both smallest and largest integers are positive (

in which case all integers will be positive).

So from this statement, we get that either all integers in set S are negative or all integers in set S are positive.

Not Sufficient.

Combining both, whether it be a set with exactly three integers or more than three integers - from second statement we know that either all integers in set S are negative or all integers in set S are positive. But if all integers become positive, then product of 'any three integers' will NEVER be negative, it will be positive and will violate the first statement. So we are left with only one case - that all integers in set S are negative.

Sufficient.

Hence

C answer.