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I have made up the sentences.

(1a) What size hats do you wear? (friends' answer: correct)

(1b) What size of hats do you wear?

(2a) What shape hats do you like?

(2b) What shape of hats do you like? (friends' answer: correct)

I have heard people say (1a) and (2a). The ones with "of" sound okay to my non-native ears. My non-native English speaking friends different answers for me. I am not sure who is correct. Please help me.

Thank you very much.

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ansonguy(1a) What size hats do you wear? (friends' answer: correct)

It's "hat", not "hats": "What size hat do you wear?" "Of" is wrong, but that doesn't stop people from using it. There are, as always, many ways to put it, for example, "What is your hat size?"

ansonguy(2a) What shape hats do you like?

"Shape" does not really go with "hats". I would expect "What style of hat do you like?" "Of" is required here. It is a different case than "size", and I don't know why.