There is a very small mistake in the original posting of the question, but the small mistake made people confused! Correct version of the question is as follows:
According to a study published in The
New England Journal of Medicine, aspirin
prevents blood clots just as well as a commonly used and more expensive blood-thinning drug does.
(A) prevents blood clots just as well as a commonly used and more expensive blood-thinning drug does
(B) prevents blood clots just as well as does a commonly used and a more expensive blood-thinning drug
(C) prevents blood clots just as well as will a commonly used and more expensive blood-thinning drug
(D) works just as well as a commonly used and more expensive blood-thinning drug at the prevention of blood clots
(E) works just as well as does a commonly used blood-thinning drug, which is also more expensive, at preventing blood clots
With reference to earlier discussions, placement of "does" is not really problematic in option B.
Here option B mentions "a commonly used and a more expensive" -- this means aspirin is compared with two different categories of drugs. But, the logical and original meaning of the sentence is to have one category of drug. Addition of "a" before "more expensive blood-thinning drug" makes option B incorrect.
If the article "a" was not there before "more expensive blood-thinning drug", option B would have been correct option as well.