There are white, red, black and blue cars . the number of each colour car is a factor of 36. there are twice as many white cars as red cars. the number of blue cars is twice that of black cars. the number of black cars is the product of two different prime numbers. the number of red cars is a square number that is not a multiple of 2. if there are 45 cars calculate how many cars each colour there are

Given:
White Car
Red Car
Black Car
Blue Car

Each color car is a factor of 36 ⇒ 2 * 2 * 3 * 3

There are twice as many white cars as red cars.
Assume Red cars is X ; then White cars is 2X.

The number of blue cars is twice that of black cars.
Assume Black cars is Y ; then Blue cars is 2Y.

The number of black cars is the product of two different prime numbers:
2 and 3 are prime numbers; they are also factors of 36. So, black cars is 2 times 3 is 6.

If Black car is 6, then blue cars is 12 (2 * 6).

Red cars is a square number that is not a multiple of 2. 2 and 3 are factors of 36. Square of 3 is 9. It is not a multiple of 2.

If red cars is 9, then white cars is 18 (2*9).

Total number of cars is 45.

White = 18
Red    =  9
Black =  6
Blue   = 12