Not ONLY will you talk to her before the test. You also have to make friends with her, make sure you talk to her early. Then After you get your sith lightsaber from the tomb of Naga Sadow and then you kill Uthar Wynn. THEN persuade Yuthura with many kind words blah blah blah, after you battle with her of course
. To make sure you make friends with her she'll call you "friend" in the earlier conversations.