Usage of "of which", "in which", "for which", "in that"?

I am generally confused when I see "of which", "in which" or "for which" instead of the plain and simple "which" as a relative clause.
For example:
Researchers have announced that the magnetic fields emitted by one manufacturer’s security surveillance system, of which type there are 200,000 worldwide, can interfere with pacemakers and that this interaction can bring on missed or irregular heartbeats, nausea, breathlessness, dizziness, and even fainting.

In this example, why can't we use a simple "which" in place of "of which"? And in general what rules govern the usage of:
1. Of which
2. In which
3. For which
4. In that

I am new to the forum, and would like to see an expert reply on this topic, as I tend to struggle when I see the above usage.

@e-GMAT. Look forward to your response.

Relative clauses can have prepositions. The relative pronoun is the object of that preposition in that case.
The prepositions are required. Think how you will frame "of which type there are 200,000 worldwide" in a sentence:

There are 200,000 worldwide "of" this type.

Can you say:

There are 200,000 worldwide this type.

No.

When the object of the preposition is a relative pronoun, the preposition will come before the pronoun.

Other examples:
It is the school to which I belong.
The boy with whom he is talking is my brother.
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We use whose with both people and things, but of which is more common with things:

The house, the garden of which sloped down to the beach, was enormous.
The house, whose gardens sloped down to the beach, was enormous.

Note that "of which" is often somewhat formal in tone.

1. The things of which we rarely speak.
2. In the meeting, we discussed three topics, the details of which are shown below.
3. The play, whose style is rigidly formal, is typical of the period. =The play, the style of which is rigidly formal, is typical of the period.

"in which" means "where", but sometimes the "where" is used colloquially, not to mean a place.

This is the city I grew up in.
This is the city in which I grew up.

With relative clauses of place and time, we can use where and when instead of preposition + which.

Tuesday is the day when (or: on which) I go to the fitness club.
The school where (or: at which) I first studied English is in Thasos.

WATCH OUT!

We use whom, not who, after prepositions and phrases like most of, all of:

That's the man to who I sold my car. [INCORRECT]
Several people came, most of who I hadn't met before. [INCORRECT]

That's the man to whom I sold my car. [CORRECT]
Several people came, most of whom I hadn't met before. [CORRECT]

We can't use that after prepositions or in non-defining clauses:

My father, that has recently retired, spends all day reading the newspaper. [INCORRECT]
This is the house in that I grew up. [INCORRECT]

My father, who has recently retired, spends all day reading the newspaper. [CORRECT]
This is the house in which I grew up. [CORRECT]
This is the house that I grew up in. [CORRECT]
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This is the house in which I grew up. [CORRECT]

What is better here - "In which" or "Where"? I think, "Where" is better here, because it is modifies place/location

Thanks a lot.

However, I notice that "In that" has a correct usage:

Deliberately imitating the technique of Louis Armstrong, jazz singer Billie Holiday’s approach to singing was to use her voice like an instrument, in that she ranged freely over the beat, flattened out the melodic contours of tunes, and, in effect, recomposed songs to suit her range, style, and artistic sensibilities.

(A) Billie Holiday’s approach to singing was to use her voice like an instrument, in that she ranged freely over the beat, flattened
(B) Billie Holiday’s approach to singing was to use her voice in a similar way to how other musicians play instruments, in ranging freely over the beat, flattening
(C) Billie Holiday approached singing by using her voice like other musicians played instruments, ranging freely over the beat, flattening
(D) Billie Holiday used her voice in the same way that other musicians use their instruments, in that she ranged freely over the beat, flattening
(E) Billie Holiday approached singing by using her voice like other musicians Instruments, ranging freely over the beat, flattening

OA is D. Can you explain? ziyuen VeritasPrepKarishma

In this case, I believe in that (=because / for the reason that) is used as an idiom. You may refer the screenshot from Oxford and Cambridge dictionary.

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i am not e-gmat, but will try to explain

prior to "of which" we have "security surveillance system"
main noun - system
system, which type there are - doesn't make any sense - right?
there are 200k types of surveillance systems, right?
therefore - of which is correct.

abhimahna, Duplicated post. https://gmatclub.com/forum/usage-of-of- ... 36334.html
https://gmatclub.com/forum/usage-of-of- ... 36337.html
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The exact example you've used here is already covered in another thread: https://gmatclub.com/forum/researchers- ... 63859.html

Check that one out, and see if it helps you understand how the "of which" works? And in general, we always recommend searching for questions and topics before posting them.
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Hey, Thanks. It was not duplicate post actually. I was Triplicate post.

I have merged all now. Thanks
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Quote from Ron

If the modifier starts with "which", it should be preceded by a comma. (in the standard American usage endorsed by GMAC, "which" without a comma becomes "that".)

The GMAT tends to write sentences in which "which" stands for the ELIGIBLE noun that's closest to the comma.
By "eligible", it means that the noun has to AGREE IN TERMS OF SINGULAR/PLURAL with the FOLLOWING VERB.

Here's an example:

The box of nails, which is on the counter, is to be used on this project.

In this case, "which" CANNOT refer to "nails", since the verb "is" is singular. therefore, the nearest eligible noun is "box (of nails)". so, "which" unambiguously stands for that.

"in which", "from which", "to which", etc. can appear either with or without a comma:
I saw a play that was reviewed in the local newspaper.
I saw a play in which one of my friends plays a starring role.
("in" + "that" = "in which")

I need to buy the assigned textbook, which contains all the problems that will be assigned in the course.
I need to buy the assigned textbook, in which all the assigned problems can be found.
("in" + ", which" = ", in which")
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See KarishmaB for a perfect explanation up top.

“On which” , “for which”, etc. may be used with or without a comma preceding it.
(Is the descriptive information essential?)

Whether you use “at which” or “for which” or “on which” depends on which preposition works best for the sentence.

These types of constructions are used when the relative clause refers to the modified noun as an object of a preposition.

The relative clause will always have its own subject, apart from the relative pronoun.

It’s a type of “sentence inversion” used in formal writing that is seen on the GMAT.

Colloquial ex: *Let us discuss the accident (that) the company is responsible FOR.

Since the relative clause has its own subject (“the company”), the relative pronoun “that” is optional.

However, the relative clause ends with a Preposition. According to many arcane prescriptive grammar rules, this would be considered a grammatical error.

A more formal sentence involves the fronting of the preposition followed by “which”, in place of “that.”

Correct: Let us discuss the accident FOR WHICH the company is responsible.

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