How did Galadriel pass the test in 'The Lord of the Rings'?

Answer 1

In 'The Fellowship of the Ring' Chapter 7 The Mirror of Galadriel, Frodo has a 'private session' with Galadriel. After showing him the magic she does (using the water surface to scry) Frodo offers her the ring if she would ask for it:

"'You are wise and fearless and fair, Lady Galadriel,' said Frodo. `I will give you the One Ring, if you ask for it. It is too great a matter for me.'"

She admits that she have wondered what she could do if the ring fell in her grasp. So much so that she had contemplated taking the ring from him.

With the offer of the ring given freely she imagines the outcome of such an event:

"`And now at last it comes. You will give me the Ring freely! In place of the Dark Lord you will set up a Queen. And I shall not be dark, but beautiful and terrible as the Morning and the Night! Fair as the Sea and the Sun and the Snow upon the Mountain! Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth. All shall love me and despair! '"

But she does not ask for the ring. She lets Frodo keep it. As he offered it freely and thereby showed that he does not have personal ambitions for the use of the ring, he has proven himself a better ring-bearer.

And as she does not ask him for the ring she has passed the test of personal ambition versus the better good:

"'I pass the test,' she said. `I will diminish, and go into the West and remain Galadriel.'"