How do you know the ratio of the cars

An auto dealer sells 40 cars, of which some are compacts, others are sedans, and still others are station wagons. Any of the following could be the ratio of compact cars to sedans to station wagons, EXCEPT:
A) 2:1:1
B) 3:1:1
C) 3:2:1
D) 3:2:3
E) 5:3:2

Think of it in "parts of 40".

In A), you have 2 parts to 1 part to 1 part, for a total of 4 parts. Since 40 is divisible by 4, it's possible.

In B) you have 5 parts. 40 is divisible by 5
In C) you have 6 parts. 40 is NOT divisible by 6
In D) you have 8
In E) you have 10

So the only one that couldn't be the equal parts of 40 is:


ANSWER

C) 3:2:1

Add the ratio numbers up and see whether the total, 40, can neatly be divided by them. If not, then some customer must've received only parts of a car, and they might notice and complain.

A., for example, gives a total of four, and 40 can be cleanly divided by that. Removing my shoes and socks allows me to compute that would produce ten. That would be 20 of one model and 10 each for the other two.

Or D. 40/8. D. would involve 15 of one type, 10 of another and 15 of the third. That's also 40.