If you keep in mind the rule concerning subject verb agreement the correct sentence is "How are your studies?" The rule states that the subject and verb must agree. If you have a plural verb, you must have a plural subject. If you have a singular verb the subject must also be singular. Subjects and verbs must also follow parallel structure and be the same tense throughout the sentence.
Also keep in mind that the statement, "How are your studies?" is not a correct formal sentence. This is a question that is worded rather awkwardly. A better way to write the sentence would be, "How are you doing with your school work?"
Being a bit of a traditionalist myself, I would throw my hat in with ladyvols1. "How is your studies" is not only awkward but is also a direct affront to the established rules of subject/verb agreement. Check out any middle school grammar book for confirmation. That said, I can understand why you would post such a question. It is becoming more and more difficult to determine what is vernacular (English B) and what is proper English (English A). There is absolutely a time and place for each, with audience and occasion being two of the main deciding factors.
"How are your studies?" I believe that that is the correct way of saying it. This is because of the verb subject agreement. The verb is plural because the subject is plural. Also, it just makes more sense and just sounds right.
The correct answer is:
How are your studies?
In this question you can see that the plural form of study is used. Therefore depending on it the adjective that support plural form is "are". If the word study had been used then adjective 'is' was supposed to be used.
The correct term is " How are your studies " because studies is plural. The other two terms can be put off as improper English because it won't make sense to the person you are asking that question to.
How are your studies is correct because studies is plural
"How are your studies?" is the correct way of saying it. This is because there must be subject and verb agreement in a sentence. In this sentence the subject is studies. Since studies is a plural subject then the verb used to describe it must also be plural. Hence the verb that must be used cannot be "is" it must be "are".