China was able to avoid imperial control in the early 20th century because
a.britain and the u.s. was opposed to outright colonization
b.europe was more concerned with the rise of japan
c.china was too far away from europe
d.russia agreed to stay out of asia
e. many westerners were sympathetic to the aims of Sun Yixian
You might want to check your text to see what it says, because many of these things could have played a role in keeping China from becoming a colony of some European power.
But I would argue that A -- Great Britain and the United States were opposed to it -- is the best answer here.
Both Great Britain and the United States wanted all countries to have free access to the market in China. It is not likely that either of these countries would have stood idle while some other country took China as a colony. Because these were probably the two strongest countries in the world at that point, people had to go with what they wanted.