Every gerund/participle ends in -ing, so you can know for sure that the answer is one of these two. Since here <em>turning </em>is used with an adverbial function (that is, it is basically an adverb - it tells us WHEN Kate bumped into David), the correct answer is B) participial.
B.to buy Santiago and himself more time to find the treasure
The dependent clause is typically in the past too. If not, this is called a tense shift and it should be avoided unless necessary.
Answer:
It seems to be a theme of ambition.
Explanation:
"it's handle torward my hand" hints the ambition to use it. The handle being toward them makes the blade much more suggestive torwards using it.