Yes, the answer is C. We need both statements to find the answer.


Statement 1:

it indicates both the Max number and Min number can be negative or Positive.

Negative * negative = positive
Positive * positive = positive

But it does not say how many number are there.

Statement 2:
It says that there are even numbers in the set.

If you multiply any even number of positive numbers, the answer will be always positive.

Also, if you multiply any even number of negative numbers, the answer will be always positive.

(-1 * -4* -5* -6 = +120)

So we need both statements to find the answer.

(1) If the product is of the greatest and smallest integers is+ve, then the integers are either both positive or both negative.

Eg. 1x7 =7, (+), -1x-7 = 7, also (+),

However, without further information about the number of integers in the list, one cannot tell the sign of the product. Not Sufficient.

(2) If there is an even number of integers in the list, the product can be either positive or negative.

Eg. 1x7 = 7 (+)
-1x7 = -7 (-)

Not Sufficient.

Considering both statements,

If there is an even number of integers in the list, and the product of the greatest and smallest integers in the list is positive, then the product of all the integers must also be positive, since the product of an even number of +ve integers is +ve, and the product of an even number of -ve integers will also be +ve.

Eg. (+)(+)(+)(+) = (+)

(-)(-)(-)(-) = (+)

Also, remember from the explanation in (1) above that since the product of the greatest and smallest integers is positive, the numbers must all be either positive or negative. You can't have (-1)(1)(2)(7) as the product because (-1)(7) = -7, which violates the requirement that the product of the greatest and smallest integers be +ve.

Both statements together are sufficient to answer the question in the stem, but neither statement alone is sufficient.

Take stmt 1)

If the product of greatest and smallest is positive then both these numbers either are positive or negative.

If they are negative then there is no telling if the product of all in the list is postive

Stmt 1)by itself is insufficient so it bolis down to B,C,E

Take stmt 2

There is a even set of elements in the list

stmt 2 by itself doesnt gaurantee the product of all elements to be positive
since the elemenst could all be positive all be negative or a combinaion of pos and neg

When we take stmt1 and stmt2 together we know the highest and lowest are both neg or both pos and if it all negative then the product of even number of negative numbers is always positive. If its all positive the the product is always positive

there fore C)

thanks for the replies. But i think we are assuming here that we have either all the integers as + or -, which is not a valid assumptions.

e.g. If we have -3,-1, 2, -5...in this case the 1st and 2nd statements get satisfied. But still we cant say that the product is +.

The argument only says list of different integers. It can be mixed one as i have mentioned above. But while answering all of you have assumed that all integers are either + or -.


Any thoughts on this?