China was able to avoid imperial control in the early 20th century becausea.britain and the u.s. was opposed to outright colonization b.europe was...

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.