"A friend of mine" of "A friend of me"

[Olaf]

English Error, Elementary Level

ESL/EFL Test #9 "Sorry, Wrong Number", question 3

Oh, aren't you Mike Fuller? A good friend of my gave me your number.

(a) aren't
(b) my
(c) me

English Error, Elementary Level

ESL/EFL Test #9 "Sorry, Wrong Number", answer 3

Oh, aren't you Mike Fuller? A good friend of mine gave me your number.

Correct entry: mine
The error was: (b) my

You have found the error but your entry is incorrect.
Oh, aren't you Mike Fuller? A good friend of my gave me your number.
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why this word correct?

Olaf

[Mister Micawber]

.
'A friend of mine; a book of yours; a class of his'-- this is how we use the possessive pronouns, Olaf.
.
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Native English teacher at Mister Micawber's