Question

The product of three integers is –216, but their sum is –23. Which of the following is not one of these three numbers? -2 -12 -6 -9

Answer 1

We can conclude that -6 is not one of these three numbers. So, the actual numbers are:

• 
  `\left(-2\right)+\left(-12\right)+\left(-9\right)=-23`

• 
  `\left(-2\right)* \left(-12\right)* \left(-9\right)=-216`

Explanation:

• The product of three integers is –216.

• Their sum is –23.

Considering the given numbers

-2 -12 -6 -9

Lets take the three numbers

-2 -12 -9

Taking the sum of -2 -12 -9

`\left(-2\right)+\left(-12\right)+\left(-9\right)`

`\mathrm{Apply\:rule\:}+\left(-a\right)\:=\:-a`

`=\:-2-12-9`

`=-23`

Therefore, the sum of -2 -12 -9 is -23.

i.e.

`\left(-2\right)+\left(-12\right)+\left(-9\right)=-23`

Taking the product of -2 -12 -9

`\left(-2\right)* \left(-12\right)* \left(-9\right)`

`\mathrm{Apply\:rule\:}\left(-a\right)* \left(-b\right)\:=\:a* \:b`

as

`\left(-2\right)* \left(-12\right)=2* \:12=24`

so

`=24* \left(-9\right)`

`\mathrm{Apply\:rule\:}a* \left(-b\right)\:=\:-a* \:b`

`24* \left(-9\right)=-24* \:9=-216`

Therefore, the product of -2 -12 -9 is -216.

i.e.

`\left(-2\right)* \left(-12\right)* \left(-9\right)=-216`

Thus, we can conclude that -6 is not one of these three numbers. So, the actual numbers are:

• 
  `\left(-2\right)+\left(-12\right)+\left(-9\right)=-23`

• 
  `\left(-2\right)* \left(-12\right)* \left(-9\right)=-216`