TRUE/FALSE by 1775 the population size of the mainland british north american colonies reached ore tha one-third the population size of England and Wales

True.

Britain's 13 North American colonies experienced an extraordinary rate of population growth. In 1700 the population was about 250,000; seven decades later there were about 2,500,000 inhabitants, a tenfold increase. This phenomenal growth was a prerequisite for a successful independence movement. In 1700 there were 20 people in Britain for every American colonist; by 1775 this ratio had fallen to 3 to 1.

From:

American Revolution - MSN Encarta (http://encarta.msn.com/encnet/refpages/refarticle.aspx?refid=761569964)

While I'm sure that the above may be close, it should be taken with "a grain of salt". The first US census was not until later, so population numbers can only be "educated guesses" based on locality census' and guesses of populations of areas where there was no census.

That in mind, though, if the question is from a text book of some sort, I'd suggest digging into it to see what the textbook publishers say is the right answer.