preposition + which, what's the role of "which"

[asker]

Sentence example:
1) The period when the great painted caves at Lascaux and Altamira were occupied by Upper Paleolithic peoples has been established by carbon dating, but what is much more difficult to determine is the use TO WHICH primitive peoples put the caves, the reason for their decoration, and the meaning of the magnificently depicted animals.
Or
2)
if you look at this post: https://www.manhattanprep.com/gmat/foru ... t1277.html
StaceyKoprince wrote: make up the extended noun phrase TO WHICH "which" refers
3)
According to public health officials, in 1998 Massachusetts became the first state IN WHICH more babies were born to women over the age of thirty than under it.
4)
In an effort to reduce the number of fires started by cigarettes, a major tobacco company is test-marketing a cigarette in which thin layers of extra paper are used to decrease the amount of oxygen entering the cigarette, thereby slowing the rate AT WHICH it burns and lowering the heat it generates.

I saw a lot of structures like these examples. They are using different prep in front of WHICH. Confused on this structure.
So how to understand the TO/IN/AT WHICH here in these sentences?
1)
I knew that TO is part of the intransitive verb phrases "refers" or "put", but for some reasons they were moved to the beginning of the noun modifier(am I right for noun modifier, or adverb modifier?), I don't know why they moved. Can anyone help to explain?

2)
And what role do these WHICH play? They are not simply "in which = when" or "at which = when."

[RonPurewal]

i have no idea how to give you a 'rule' in words here. furthermore, even if such a rule did exist, the phrasing would be so long/clumsy/awkward/mystifying as to be useless anyway.

...but, if you just memorize a few EXAMPLES of these patterns, you should be able to recognize (and construct) similar examples with surprising ease.
(nb: this is how ALL human brains learn ALL languages. think about how you learned your first language—whatever that language might be—as a kid. thousands upon thousands of examples; zero rules. if you ever learned 'rules' you learned them only in retrospect.)

i store my jewelry in this box.
...so, this box is the box in which i store my jewelry.

i buy my groceries at Ralphs (= a grocery store in downtown LA).
...so, Ralphs is the store at which i buy groceries.

a payment is late if it is received after the 15th of the month.
...so, the 15th is the date after which a payment is late.

[RonPurewal]

by the way, if the above examples seem seem unfamiliar or 'weird', then you can lay the blame squarely on the shoulders of SPOKEN english, which generally doesn't contain such things (unless the speech is ceremonious, florid, or just plain snooty).

people don't SAY 'the box in which i store my jewelry'; rather, they SAY 'the box i store my jewelry in'.
similarly, people don't SAY 'the store at which i buy groceries'; rather, they SAY 'the store i buy groceries at'.
...but once you learn the correct way to construct these things in formal writing, you should find that they aren't terribly hard to understand.

[RonPurewal]

They are not simply "in which = when" or "at which = when."

now this ^^ i don't understand.
'when' is a totally different animal, altogether unrelated to these things. what would make you think there's a necessary relationship (or, for that matter, any relationship)?

[asker]

They are not simply "in which = when" or "at which = when."

now this ^^ i don't understand.
'when' is a totally different animal, altogether unrelated to these things. what would make you think there's a necessary relationship (or, for that matter, any relationship)?

The thought process for this equation is
1) learnt from some old wrong grammar rules based technique. They simply categorize "in which = when" for students to understand the sentence.
2) when I try to replace "in which" to when, I found it represent the same meaning. so I thought it was justified. But maybe I'm wrong,

[RonPurewal]

They simply categorize "in which = when" for students to understand the sentence.

really? someone seriously wrote this down as a ‘rule’?
um…
wow.

i mean, there’s a ton of bad SC advice on the internet. (as my grandfather always said, “free advice is usually worth exactly what you paid for it.”)
…but i’m not sure i’ve EVER seen any ‘advice’ quite as bad as this.

’in which = when’ is amazingly easy to disprove. if you just flip through a few pages of OG SC problems, you can fill a whole bag with counterexamples.

in the 2016 OG, i found five counterexamples (SC #64, SC #80, SC #109, SC #128, and Diag #35) in less than 10 minutes. remember, just ONE of these is enough to disprove this 'rule'... and, in just a few minutes, i found five.

why are people making up ‘rules’ that can be shot down—repeatedly—by 10 minutes of simple research?
):

[asker]

I just found a post here: [redacted]

"It's considered incorrect to end a sentence with a preposition.
For example, we shouldn't say:

""I just visited the school that I went to.""

Instead, we should say:

""I just visited the school to which I went.""

Just as it's improper to end a full sentence with a preposition, it's improper to end a phrase with a preposition.

So, ""that North Americans are exposed to"" should be ""to which North Americans are exposed""."

I think it related to this topic, and the reason for this kind of "prep + which" is because we cannot put preposition at the end of a sentence. To put preposition ahead, we have to use "which" as a relative pron following the prep?

[RonPurewal]

do not post links to other forums please.

[RonPurewal]

it's best to explain this sort of thing by example.

i wrote about this whole thing here:
https://www.manhattanprep.com/gmat/foru ... ml#p101503

[asker]

i have no idea how to give you a 'rule' in words here. furthermore, even if such a rule did exist, the phrasing would be so long/clumsy/awkward/mystifying as to be useless anyway.

...but, if you just memorize a few EXAMPLES of these patterns, you should be able to recognize (and construct) similar examples with surprising ease.
(nb: this is how ALL human brains learn ALL languages. think about how you learned your first language—whatever that language might be—as a kid. thousands upon thousands of examples; zero rules. if you ever learned 'rules' you learned them only in retrospect.)

i store my jewelry in this box.
...so, this box is the box in which i store my jewelry.

i buy my groceries at Ralphs (= a grocery store in downtown LA).
...so, Ralphs is the store at which i buy groceries.

a payment is late if it is received after the 15th of the month.
...so, the 15th is the date after which a payment is late.

In OG2016, SC80, it's not following this rule.

“in which” is way too far away to refer to “companies”, according to your rule: "this company is the company in which standard business transactions are handled via computer rather than on paper." should be equal to "standard business transactions are handled via computer rather than on paper in this company", obviously no problem, right?
OK, if so, "where" should be replaceable for "in which": this company is the company where standard business transactions are handled via computer rather than on paper.

But the OG said where is wrong: "Where is a nonstandard way to refer to a noun that does not name a location."
1) company is a location, why not? e.g. -Hi Boss, where are you now? - I'm now at a special location, the location is our company.
2) if "where" is wrong here, since "where" equal to "in which" in my previous analysis, does that mean, OG implies your rule for the usage of "in which" is also wrong?

by the way , in this post:
https://www.manhattanprep.com/gmat/foru ... tml#p41392
you mentioned "we have just learned that "where" also applies to a certain segment of words that do not represent physical locations.", but OG said cannot refer to a location. Does this sound contradictory?

[RonPurewal]

in that example, 'in which' refers to the single noun that is directly in front of it. so there is no problem at all.