Usage of rare, sparse or scarce

[Sophie]

Please help me to choose the right answer in this sentence.
Her daughter is of .... beauty.
a. rare
b. sparse
c. scarce
d. all are correct
Thanks a lot.
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On earth there is nothing great but man, in man there is nothing great but mind.

[Mister Micawber]

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How about trying yourself first? Hint: Is the girl beautiful?
.
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Native English teacher at Mister Micawber's

[Sophie]

Oh, I think this sentence means the girl has a great beauty and very few people are more beautiful than her.
"Rare" is just concerned with the frequency of action or occasion. "Sparse" just describes the density. So the answer can't be a, b or d. I think the answer is c.
What do you think about it?
_________________
On earth there is nothing great but man, in man there is nothing great but mind.

[Abraaocoutinho]

I think the answer would be "rare" because both "scarce" and "sparse" give an idea of lack. So, i think her beauty is rare because it is uncommon.
that is my opinion.
let's hear a 3rd one.
thanks.

[Sophie]

Well, I think I'll take it into consideration.
Anyway, thank you very much, Abraaocoutinho!
_________________
On earth there is nothing great but man, in man there is nothing great but mind.

[Mister Micawber]

.
'Rare' is indeed the answer. Here, 'rare' = 'marked by an uncommon quality; especially superlative or extreme of its kind ("What is so rare as a day in June-J.R.Lowell")'.
.
_________________
Native English teacher at Mister Micawber's

[Sophie]

Well, thank you.
_________________
On earth there is nothing great but man, in man there is nothing great but mind.