Similar to Countif naive souls are happy with Sumif if they only need to apply one condition.

Please see my example on the left.

But as soon as you face two or more conditions which you want to apply with logical AND's or OR's, you are in trouble again.

SUMPRODUCT is your solution here.

The example on the left shows the sum of all Ford cars from USA (2,000 - this a logical AND) and the sum for all cars which are a Ford or from USA
(11,400 - this is a logical OR).

Please note that I suggest NOT to take SUMPRODUCT as a holy grail. I use this example just as an evolutionary argument. Please read additional material on SUMPRODUCT here.