Singular or plural for [type] in [type of gems]

Suppose that your friends are showing you some gems that are all identical on a table. You have a question for him.

(1) What type of gems are they? (I made it up myself.)

(2) What types of gems are they? (Some of my non-native English speaking friends revised my question to this one.)

(3) What type of gem is it? (My other non-native English speaking friends revised (2) to this one.)

I think my sentence is correct. "Type" is singular because all the gems are exactly the same, so there is only one type. "Gems" is plural because you are looking at some gems. I think (2) is wrong because the plural form of "type" suggests there is more than one type. I also think (3) is wrong because the singular form of "gem" suggests there is only one on the table. I am not sure which sentence is correct. Please give me your answer. Thank you very much.