UNSTOPPABLE12You're right that there is a problem with "it was during his lifetime." This appears to be making a comparison we don't want. "
When did C's stories make him popular? It was in his lifetime, not after his death." The contrast we really want is between now, when Chekhov is better known for his plays, and his lifetime, when he was popular for his stories." I'd say that this is the most critical flaw in A.
The issue with "by far" is more a matter of convention. Since "by far" is a prepositional phrase, we would usually put it after the term it modifies ("better known") rather than before. "Far" is just working as a simple adverb, so it goes before the term. A few examples:
The remake is far superior to the original.
The pool installation was far more expensive than I expected.
Sam Cooke was a greater singer by far than anyone on the radio today. (Note that "by far" modifies "greater," even though "singer" gets in between. It's an adverbial modifier, so we don't always have to put it right next to what it's modifying. In fact, in a case like this we just can't.)
Your score exceeds the required minimum by over 20%. (This isn't just about "by far." We put "by 20%" after the whole phrase because it would be disruptive (but not necessarily wrong) to put "by 20%" after "exceeds." It would be flat-out wrong to place "by 20%" before "exceeds."
Here's another official GMAT question that uses the same split. Try it before reading the bit below:
https://gmatclub.com/forum/some-scienti ... 20827.html**
Notice that in that question, the "by far" answers both have other bigger flaws, just as in the Chekhov question. However, there's no real need to say "exceed by far" when we can say "far exceed," so GMAC could also say that the construction in the right answer is preferable.