If P is the product of all the numbers in set S, is P positive ?

Question

(1) The number of negative numbers in set S equals to the number of positive factors of 169
(2) All the integers in set S are non zero.

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divyadna · Answer

P is the product of all the numbers in set S, is P positive ?

Is P>O?

(1) The number of negative numbers in set S equals to the number of positive factors of 169

169=13^2

Positive factors of 169 are 1,13, and 169.
So, there are three negative numbers in set S. We neither know how many positive numbers are there in set S nor know whether 0 is there in the S or not.

Statement I alone is insufficient.

(2) All the integers in set S are non zero.

This statement tells us that P is not equal to zero but since we do not know the numbers of positive and negative numbers, we cannot say whether P is positive.

Statement II alone is insufficient.

Combining statement I and II

Set S has 
I) 3 negative numbers
II) no 0 
Now, whatever be the number of positive numbers, P will always be negative.

Statement I and II combined together are sufficient.
Option C is the answer

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Afn24 · Answer

Set S has 
I) 3 negative numbers
II) no 0 
Still we aren't sure about the number of positive numbers.

E.g. If there are equal number of positive numbers, P is positive.

If not, P is negative.

Statement I and II combined together are still insufficient.
Option E is the answer

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Why would it make any difference how many positive numbers there are? 
If the product of 3 negative numbers is negative then no matter how many positive numbers are multiplied by it. The product will still be negative

Bunuel · Answer

The question is tricky! Anyone else want to try?

szcz · Answer

Great Question. Just needs a little presence of mind.

(1) The number of negative numbers in set S equals to the number of positive factors of 169

From this statement we know that the number of negative number is 3. We are only concerned with the negative numbers and if there is a 0. Actually in this case whether a 0 exists or not will not matter as we can see below. Positive numbers cannot change P.
We will have 2 cases.
Case 1: Set S contains 0. In this case P will be 0. But is P positive. The answer is No.
Case 2: Set S does not contain 0. I this case P will be negative (since we have odd number of negatives). But is P positive. Again the answer is No.
Hence, both cases give the same answer and therefore statement 1 is sufficient.

(2) All the integers in set S are non zero.
This definitely tells us about the 0 in the set but nothing about the negative numbers. Hence, insufficient.

Answer is Option A.

Archit3110 · Answer

Target whether P which is product of all numbers in set S +ve
#1
The number of negative numbers in set S equals to the number of positive factors of 169
13^2 : 3 factors 
So we can say conclusively that product P will be either 0 or -ve but not +ve Sufficient

#1 All the integers in set S are non zero.

Count of -ve integers is not known for even -ve count we get +ve and for odd -ve
Insufficient

OPTION A

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Happysumit007 · Answer

0 is not a positive number. C would be correct answer. if any wants , google it for reference.

If P is the product of all the numbers in set S, is P positive ?

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