gmatblood wrote:A set consists of of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive

(2) There are an even number of integers in the list

IMO E. Whts the OA?

Interpretation of Question

Lets first arrange the integers in the set in ascending order
S={a,b,c,d,e,f,g,...............x}
For product to be positive we need even or 0 number of negative integers.

so we can rephrase the ques as

Are there any negative integrs in the set? If yes, is the number of negative integers even?


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

a*x is positve

this means either all integers are positive or all or negative and a is not equal to 0.
but we dont know, if the number of integers is even.

Insufficient

Statement 2:
There are an even number of integers in the list

This tells us nothin about the no of negative integrs

Insufficient


Combining 2 statements
From S-1,
All integers are either only negative or only positive.
From S-2,
There are even number of integers.

If all integers are positive,then the product will ofcourse be positive

If all integers are negative, and the number of integers is even, the product will be positive.


Hence, Option C is the answer.

Rijul great idea and superb approach towards the problem..
but how can you prove that you did not assume that the elements in the set are in ascending order?? please prove this.. thanks in advance

rijul007 wrote:Interpretation of Question

Lets first arrange the integers in the set in ascending order
S={a,b,c,d,e,f,g,...............x}
For product to be positive we need even or 0 number of negative integers.

so we can rephrase the ques as

Are there any negative integrs in the set? If yes, is the number of negative integers even?


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

a*x is positve

this means either all integers are positive or all or negative and a is not equal to 0.
but we dont know, if the number of integers is even.

Insufficient

Statement 2:
There are an even number of integers in the list

This tells us nothin about the no of negative integrs

Insufficient


Combining 2 statements
From S-1,
All integers are either only negative or only positive.
From S-2,
There are even number of integers.

If all integers are positive,then the product will ofcourse be positive

If all integers are negative, and the number of integers is even, the product will be positive.


Hence, Option C is the answer.

how can you prove that you did not assume that the elements in the set are in ascending order?? please prove this.. thanks in advance

I dindnt assume anything. I arranged them myself as a part of the solution.
Changing their order would have no affect on their product.

just like
a*b*c*d = b*d*c*a = c*a*b*d

Rijul great idea and superb approach towards the problem..

Thank you