Positive Integers

relaxin99 wrote:A certain list consists of several different integers. Is the product of all the integers in te list postive?

(1) The product of the greatest and smallest of the integers in the list is positive
(2) There is an even number of integers in the list



The answer is C, i chose E...can you someone please explain

From (1) either both greatest and least are positive or both are negative.

If the list is 1, 2, 3, 7, 9, 20 , product of least and greatest =20

if the list is -5, -3, -2, -1 then the product = -5 * -1 =5


So it is confirmed that all numbers will have same sign.


From (2) is the number of such numbers is even (so list has 2, 4, 6, 8 such numbers) . this is not sufficient.

Together, product ot list of even numbers with same sign (positive or negative) is always positive.

Example: -5, -3, -2, -1 = +ve

( product of even number of negative integers is even.)

(C)

St1: we know that all the numbers are of the same sign. Either all are positive or all are negative. Hence insuff.

St2: The total number of integers is even.
2*-1*3*4 = -24; 2*1 = 1...insuff

combining 1&2

the product of all the integers will always be positive in this case.

example: -2*-1*-3*-4 = 24
2*1 = 2 ... suff.

So C.