S is a finite set of numbers. Does S contain more negative

[agalstia]

S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.



OA is E

I chose A because I believed that Statement 1 was sufficient to conclude that there were more negative numbers in set S since their product was negative. I understand that statement 2 does not help at all. So, why is the answer E?

[gokul_nair1984]

S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

Let's consider Statement 1:
To get a product of -1200, we can have the following sets of numbers,
-600, 1,2 (Product= -1200; 2 positive and 1 negative)
-600,-2,-1 (Product= -1200; 0 positive and 3 negative)

So 1 is insufficient as both cases are contradictory(you can have a greater number of negative or positive numbers depending on the numbers you pick)

Let's now consider Statement 2:

I understand that statement 2 does not help at all.

Great!

Considering both statements together,

the 6 numbers whose product is -1200 can be 5 negatives and 1 positive or 5 positives and 1 negative

For eg:-1,2,3,4,5 and 10 or
-1,-2,-3,-4,-5 and 10.

So C is also insufficient and hence, the answer is E- Hope this helps!

[hardik.mehta007]

1) -1200, any odd no of negative numbers in the set will make the product of all numbers negative. The statement does not provide any information about no of negative numbers. it could be -1 , 1200 or -1, 2 ,600 or -1, -2, -600.
NOT SUFFICIENT
Eliminate A, D
2)
You don't have any information about negative numbers
NOT SUFFICIENT
Eliminate B

Coming two statements: There could be one, three or five negative numbers so that multiplication of all numbers would be negative.

No of negative nos = 1, 3, 5 not sufficient to answer the question.

Eliminate C

Answer = E

S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.



OA is E

I chose A because I believed that Statement 1 was sufficient to conclude that there were more negative numbers in set S since their product was negative. I understand that statement 2 does not help at all. So, why is the answer E?

[RonPurewal]

the above solution is nice.