Data Sufficiency

Hi All,

I am posting a GMAT Prep DS problem. Requesting someone to explain the problem

The problem is asking us to find out whether the product of numbers in a set is positive or negative. now this can be answered if you know following things

1. the size of the set i.e set of 2 numbers or set of 3 and so on, and
2. How many numbers are positive and how many are negative in the set

Now as per statement a) you can not come to a conclusion bcoz you dont know the size of the set. hence Not Suff
With statement b) you know that set can be of 2 numbers or 4 or 6 and so on but you dont know that how many numbers are negative. hence, NOT Suff

Now when you combined two statement, a & b, you know that set is of even no of digits and 1st and last one can be negative or positive but you still dont know that rest of the numbers can be split up in negatives and positives. So there can be a chance if the set is of 6 (removing 1st and last) you are left wih 4 numbers and in this 3 can be negative or 2 can be negative. So i chose E

But OA say C is the right answer.

Now when you combined two statement, a & b, you know that set is of even no of digits and 1st and last one can be negative or positive but you still dont know that rest of the numbers can be split up in negatives and positives. So there can be a chance if the set is of 6 (removing 1st and last) you are left wih 4 numbers and in this 3 can be negative or 2 can be negative. So i chose E

Considering the Lowest and Highest as First and Last respectively is the Mistake you did

(1) Lowest * Greatest = +ve

So, Lowest(L) and Greatest(G) either both are +ve or both are -ve.

Both Lowest and Greatest positive means all the integers in the list are positive as
0 < Lowest < All other integers < Greatest

Both Lowest and Greatest negative means all the integers in the list are negative as
Lowest < All other integers < Greatest < 0

When we consider L and G to be +ve then we can say the product of all elements can be +ve. ( 0 < L < G )
When we consider L and G to be -ve then the product of all integers depends on the total number of integers present in the list. If Odd then required product is -ve, Even +ve.

Not sufficient.

(2) Number of integers are even.

Not sufficient.

Combine both,
for all even +ve integers the product is +ve.
and
for all even number of -ve integers the product is +ve.

Sufficient.

Correct Answer is C

As rightly pointed out i misunderstood Greatest and lowest to 1st and last.

Thanks Shoven and Rahul