what is the difference between wearing the black shirt, Joe

In terms of GMAT grammar, (a) and (b) are entirely equivalent, interchangeable, two perfectly fine ways to say the same thing. For our purposes, there is absolutely no difference between them.

It's like (3 + 5) vs. (5 + 3) --- the order changes nothing.

Does that make sense?

Mike

First of all, I would say both of these sentences are completely correct.
(a) Wearing the black shirt, Joe kills the snake.
(b) Joe, wearing the black shirt, kills the snake.

but I would say this sentence is incorrect:
(c) Joe wearing the black shirt kills the snake.

Thank you expert.
I agree that a) and b) are the same.

but I think there are huge difference between a or b and c.

I think that in a and b, "wearing..." modfies the whole clause and refers to the subject. "wearing..." in a or b is adverbial. in c, "wearing..." modifies only the subject and is totally a adjectival.

it is clear that in a or b, killing has some relation with the wearing. the write means that wearing a black shirt help or is good for the killing.

in c, wearing is used to mean who do the killing because there are many persons there.

is my thinking correct?

Dear Vietmoi,
I'm happy to respond.

What you are exploring here is a grammatical/logical distinction with a few names. It may be called
"restrictive" vs. "non-restrictive" modifiers
"vital" vs. "non vital" modifiers
"mission critical" modifiers vs. (?) "not critical" (?) -- MGMAT terminology
See these two blog posts for a thorough distinction:
https://magoosh.com/gmat/2012/that-vs-which-on-the-gmat/
https://magoosh.com/gmat/2012/gmat-gramm ... modifiers/

If a modifier is vital, or restrictive or mission-critical, then it is essential for establishing the identity of the noun ---- if we dropped the modifier from the sentence, we would have no idea to which noun the sentence referred. This kind of modifier is never set off by commas.

If a modifier is non-vital or non-restrictive, it is not essential for establishing the identity of the noun, but instead, it simply provides extra descriptive or informative detail. This kind of modifier is always set off by commas.

Ordinarily, a name is enough to establish a person's identity. If we say "Joe", it most contexts it would be perfectly clear from that name alone who we meant. Thus, the modifier "wearing the black shirt" would purely be descriptive, and not at all essential for identity. Thus, under ordinary circumstance, versions (a) & (b) would be correct, and version (c) would be incorrect.

The exception would be some sort of context in which, for example, there were several people named Joe --- say, Joe wearing the black shirt, and another Joe wearing the green shirt, and another Joe wearing plaid, and etc. etc. One of these Joe's kills the snake. Now, if we say ...
Joe killed the snake.
that would create ambiguity, because we could be referring to any one of a number of Joe's. We need a vital noun modifier to clarify which Joe killed the snake. In this case, (a) & (b) would be incorrect, and only version (c) would be correct.

Remember: Logic trumps grammar. If the logic of the situation changes, than what is grammatically correct will have to change.

Does all this make sense?
Mike