Data Sufficiency

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.

hi guys, can you help me understand this DS?
the answer is C and i dont understand why because i think it should be D
this is how i solved it.
1. is not sufficient because s=-1,-2,-3, thus its product<o
s can be 1,2,3 thus its product can be positive.
2. there are an even number of integer in the set.
S= -1,2,-3,-4 its productive is still negative
and S=2,1,3,5 its productive is still positive
even 1+2 cant be sufficient.
i dont understand how it could be C? how could be C when it says nothing about how many negative/positive numbers in a set???

diebeatsthegmat wrote: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.

Ok, so A is insufficient, because the product of the greateast and smaller integers could be positive in the following 2 scenarios:
a) the smallest and greatest numbers are both positive, in which scenario the product of all elements in Set S will also be positive,
b) the smallest and greatest numbers are both negative, which will result in their product being positive. BUT if the number of elements in Set S is odd, then the product will be positive, while if the number of elements is even, the product of all elements in set S will be positive.
So A alone is insufficient.

B tells you that there are an even number of integers in the set. But it tells you nothing about the values.
So, B alone is insufficient.

Together, A and B are sufficient. Since B tells you that the number of elements is even, so under both scenarios (a and b listed above), the product of all elements in Set S will be positive. Hence, C.

Hope this helps.

My two cents;

One important number's property principle to remember, the product of a set of integers will be even if the number of negative numbers in that set is 0 or even. Rephrase this question, is there an even number of negative numbers in the set (or none at all).

a. tells us that the first and last integers must both be negative or both be positive. This tells us nothing of the number of integers in the set. Insufficient.

b. There are an even number of integers in the set. If the set are all positive then the product is positive. If there are all positive integers but one -1 in the set, then will be negative. Thus b is insufficient.

Put them together, all of the integers are either positive or all negative and there are an even number of integers in the set. Either way their sum will be even because if they are all negative there is a even number of them which will make them positive. C, both together sufficient.

Hope this helps.

Thanks,

Jared

is the product of all integers in set s positive?

say s=( -2,-3,-5) s=(-2,-3,-4-5)

1.smallest*greatest=positive


product of all negative or positive so not suff

2.there is an even no of integers in the set

s= (1,2) s=(-1,1,1,2)

it may be positive or it may be negative hence not suff

combine its s=(-1,-2) s=(-1,-2,-3,-4) in any case its positive so suff hence C

im also confused by this one... They never give us the number of negatives or positives in the set...

Combined we only know two things that the greatest multiplied by the least number are positive and also that the total integers in S is an even number...


combine its s= (1,-2,3,4) the first and last are still positive and we have an even number of integers in the set however there is only on negative number..

Struggling with this one.....

s=(1,-2,3,4)

boss product of smallest and greatest integers should be positive

smallest=-2 and greatest=4 product = -8 its not the correct set

pradeepkaushal9518 wrote:s=(1,-2,3,4)

boss product of smallest and greatest integers should be positive

smallest=-2 and greatest=4 product = -8 its not the correct set

i think i need a couple of hours /days to think of this. i am still confused.

I think i got it now... the set has to be in order...

If the least number is a negative number then the greatest number must also be negative... Because the product of the greatest and smallest must be positive...

This ensures that all the numbers in the set are negative since the numbers need to be put in order from least to greatest..

Thanks pradeep!

C and following is explanation for C:

The product of smallest and largest number in set is positive. so either both smallest and largest number are positive or both the smallest and largest are negative.
Now, if both the smallest and largest are positive then the entire items in the set are positive and hence the product would be positive.
But, if both the smallest and largest number are negative then odd number of items in the set would make the product of all the items negative while even number would make the product positive.
At this point, statement number II comes to our rescue. Now we know that the number of items are even, so the product would always be positive.

And note that the items not necessarily be in order.

got ya the numbers dont need to be in order but if the smallest is negative then the greatest also has to be negative? there fore all the numbers in between are negative??