That/which usage

"That" is used for essential modifiers, but "which" is used for non-essential modifiers. Non-essential modifiers can be removed from the sentence without losing the main meaning, but essential modifiers can't be.

The most memorable description I've read of this is from "Woe Is I," a quite readable grammar book. I'm basing my examples on the examples from that book.

Essential modifiers:
The mouse that was killed in the mousetrap is grey.
The contestant that went on to win the Spelling Bee is from Ohio.
Any house that has shoddy plumbing will usually have mold.

See what happens when the essential modifier is removed:
The mouse is grey.
The contestant is from Ohio.
Any house will usually have mold.
Note that the meaning is either lost (the death of the mouse), hidden (which contestant specifically?), or distorted (all houses don't usually have mold, just some)!

Non-essential modifiers:
The mouse, which is grey, is about to eat the cheese on the mousetrap.
Our house, which has mold, obviously has a plumbing problem.
Note that when you take the underlined modifiers out, the overall meaning of the sentence remains intact. The commas are another clue that the "which" modifier is somehow optional in the overall sentence.

For the record, with commas, a “who” modifier (i.e. like “which,” but for referring to people) is similarly non-essential:
The contestant, who is from Ohio, will go on to win the Spelling Bee.


But, however, and although are similar in meaning: they all indicate a contrast or alternative. I’m hesitating to dictate a rule, because I think all three are probably used in a variety of ways, and I’d probably omit some exception.

However ( ), I think “but” is best used in mid-sentence (often following a comma), whereas “however” and “although” can be found mid-sentence but would also be allowed to begin a sentence.

I can’t recall any OG/GMATPrep question that splits on the choice or placement of this type of word.