Question

What will be the sign of the product of 8 negative and 11 positive integers


​

Answer 1

positive sign will be there because the negatives are in even no. and if they are in even quantity then positive sign remains

Answer 2

The answer is negative. Odd numbers of negative integers when multiplied yield negative integer only. Consider an integer -x = (-1)*x. Let -y be another integer.

Then product of -x * -y = (-1)^2* xy = xy

similarly - x* -y* -z = (-1)^3* xyz = -xyz

-x*-y*-z*-s = (-1)^4* xyzs = xyzs

proceeding same way, you will observe that multiple of odd negative numbers are resulting in negative digit while multiples of even negative numbers will result in positive digits. A digit when multiplied by positive numbers, the sign of the resultant digit wont change. Hence the answer should be a positive.