I wonder which of the two is correct:
- I have a red and a blue car.
- I have a red and a blue cars.
or
- Everyone has a left and a right arms.
- Everyone has a left and a right arm.
My (non-native) inclination would be for option 1, as it sounds better. On the other hand, in the following examples, the plural sounds better to me.
But are they correct?
"A" is singular: You can't use "cars" and "arms." "A red car and a blue car" and "a left arm and a right arm" indicate two cars and two arms. "Red and blue cars" and "left and right arms" have indeterminate numbers.
There are two problems here; one is structural and the other is semantic. The reason why it's wrong to say "I have a red and a blue cars" is structural; the sentence has an unwritten but understood instance of the word "car" after the word "red". This sentence asserts that you have two cars, one red and one blue. The example "I have old and new cars" (when you have a total of two of them) is more problematic. The meaning is, at best, ambiguous, since it could certainly mean that you have two or more of either. A careful writer might want to avoid ambiguity. The sentence "Everyone has left and right arms" is similarly flawed, but appeals more to the native ear, due to the fuzziness of the word "everyone", which conveys a collective meaning, even though it literally means "every one" and is indisputably singular. It also gets a pass because it states the obvious, so the ambiguity isn't taken seriously.
If there is a single noun phrase referring to several things, it's plural. If there are several noun phrases, each referring to one thing, each of the noun phrases is singular. So, it's all about noun phrases, and how many of them there are.
An article starts a noun phrase, so in straightforward cases, you can count the articles to tell how many noun phrases there are. (Some noun phrases don't have articles.) In "Everyone has a left and a right arm" there are two articles in the object, so there are two noun phrases coordinated: [[a left (arm)] and [a right arm]]. In "The left and right arms are both necessary" there is just one article in the subject noun phrase, so there is just a single plural noun phrase, whose noun head is modified by a coordination of two adjectives: [the [left and right] arms], and this is why that noun phrase is plural and its head noun "arms" must be plural.
In ordinary cases of coordination, two things of the same category are connected by "and" to form a new phrase of that same category. That's why when two noun phrases, each with its own article, are connected with "and", the result is a noun phrase, and why when two adjectives are connected with "and", the result is an adjective. People with training in traditional grammar may resist calling a multi-word constituent like "left and right" an adjective, but they ought to get used to it.
Everyone has left and right arms. [This is correct]
I have old and new cars. (when I only have only one old car and one new car) The part of your statement in brackets is correct - I have one old car and one new car. or I have two cars. One is old and one is new.
The left and the right arms are... If you are referring to the plural and this is a continuation of the first sentence, then arms is correct. if you are only talking about one person, it should be arm.
Does this help?
I have a left and a right arm.
I have left and right arms.
The indefinite singular article 'a' requires the noun to be singular.
You could expand for clarity.
Everyone has two arms: one left and one right. Everyone has both a left and a right arm.
