Is the product of all integers in a set S positive?
a. The product of the smallest and greatest integers is positive.
b. There are an even no. of integers in the set.

Answer is c. ?

thx
P

Question Stem: Is the product of all integers in a set S positive?

Statement 1:The product of the smallest and greatest integers is positive.

This means that either the smallest and largest numbers are negative or the smallest and largest numbers are positive.(-ve*-ve=positive). In other words, All the numbers in the set are either positive or negative.

Case 1:Let the set be -1,-2,-3( Only 3 numbers)
smallest * Largest =positive(-3*-1) but product(-6) is negative. Thus No( Yes/ No Type DS Question)

Case 2:Let the set be 1,2,3( Only 3 numbers)
smallest * Largest =positive(3*1) and product(6) is positive. Thus Yes

Hence Statement 1 is insufficient.


Statement 2:
There are an even no. of integers in the set.

Case 1: Let the set be 1,2,3,4....Here Product(24) is positive. Hence Yes
Case 2: Let the set be -1,2,3,4...Here the product(-24) is negative. Hence No

Therefore, Statement 2 is insufficient

Combining both statements we again get only 2 cases,

If smallest and Largest numbers are positive and the set were to comprise even number of digits it could be:
eg:1,2,3,4-----Here Product has to be positive


If smallest and Largest numbers are negative and the set were to comprise even number of digits it could be:
eg:-10,-8,-5,-4,-2,-1--Here Product will again always be Positive

Hence C is the right answer

Gokul,
what if the set has an odd no. of -ve nos. in addition to even nos.?

thats why i chose my answer.

P

I just did not understand your question. Could you please elaborate.

here's a big thread about this problem:
a-certain-list-consists-of-several-different-integers-t1002.html