[mormegil]

I think we need to establish this before it's discussed at any real length because many of the answers are in the books.

'What did you blush for, Sam?' said Pippin. 'You soon broke down. Anyone would have thought you had a guilty conscience. I hope it was nothing worse than a wicked plot to steal one of my blankets.'

'I never thought no such thing,' answered Sam, in no mood for jest. 'If you want to know, I felt as if I hadn't got nothing on, and I didn't like it. She seemed to be looking inside me and asking me what I would do if she gave me the chance of lying back home to the Shire to a nice little hole with -- with a bit of garden of my own.'

'That's funny,' said Merry. 'Almost exactly what I felt myself; only, only well, I don't think I'll say any more,' he ended lamely.

All of them, it seemed, had fared alike: each had felt tht he was offered a choice between a shadow full of fear that lay ahead, and something that he greatly desired: clear before his mind it lay, and to get it he had only to turn aside from the road and leave the Quest and the war against Sauron to others.

--The Mirror Of Galadriel

I see here that it was a test of their true resolve. They have just passed through grief and anguish and now Galadriel can offer them what they most desire and to obtain it would be easy. How would we fare in a similar situation. I think Tolkien is attempting to illustrate that the road less travelled or often times the more difficult course is the choice best chosen.

I believe it can be inferred from the following quote that all save Boromir passed the test.

'To me it seemed exceedingly strange,' said Borormir. 'Maybe it was only a test, and she thought to read our thoughts for her own good purpose; but almost I should have said that she was tempting us, and offering what she pretended to have the power to give. It need not be said that I refused to listen. The Men of Minas Tirith are true to their word.' But what he thought that the Lady had offered him Boromir did not tell.

--The Mirror Of Galadriel

Boromir's reaction, to me, demonstrates his giving in to the 'temptation' as he put it, though it should not be correctly attributed to Galadriel. Perhaps she was able to get to their sould and find what most would tempt them to turn back and offer it to them. Samwise, the stout hearted, was the only one who said with any certainty what it was he desire, and I believe he did because how simple and innocent his desire is. Others, such as Boromir obviously had a far more nefarious desire, specifically for the ring. Galadriel, in my opinion, offered the ring to Boromir but his promise to be true to his word was true in a sense that he would stick to the quest, that is what he gave his word on; however he knew that by staying on this quest an opportunity may present itself where he could take possesion of the ring.