Question

Eighteen integers are multiplied together. What will be the sign of their product, if :
(i) 15 of them are negative and 3 are positive ?
(ii) 12 of them are negative and 6 are positive ?
(iii) 9 of them are positive and the remaining are negative ?
(iv) all are negative ?

Answer 1

Let the positive numbers be $1$ and negative numbers be $-1$

Now,

$\left(i\right)(-1{)}^{15}(1{)}^3=-1\left(ii\right)(-1{)}^{12}(1{)}^6=1\left(iii\right)(-1{)}^9(1{)}^9=-1\left(iv\right)(-1{)}^{18}=1$