relative clause or participle phrase

Question

Today my English teacher(not a native) used the sentence below to introduce the idea of relative clause:

People will buy the classics based on her recommendation but sales won't reach the kind of numbers achieved in the first book club.

My teacher explained that the sentence above is a relative clause because which were is originally placed before achieved , and numbers is modified by "which were achieved in the first book club."

People will People will buy the classics based on her recommendation but sales won't reach the kind of numbers (which were) achieved in the first book club.

My teacher said that which were is omitted in the sentence because grammar rule allows, and the omitted which represent numbers. So, the relative clause part of the sentence can be seen as : Numbers were achieved in the first book club.

But my friend told me that the teacher is partly wrong because there is no such thing as omitting which were or that "numbers which were achieved" is transformed into "numbers achieved",
the term for this is called participle phrase. But my friend said that relative clause performs the same function as participle phrase, and the meaning does not differ, so the teacher isn't completely wrong.

So I am really confused because I was given two different thoughts,
at this point I don't know whom to trust, which one is right and which is wrong?

Answer 1

People will buy the classics based on her recommendation but sales won't reach the kind of numbers (which is) achieved in the first book club.

It is perfectly reasonable to say that "which is" is omitted in the sentence.¹ Some linguists call this 'whiz-deletion' or 'relative-clause reduction'.

However, the modern reference grammar, The Cambridge Grammar of The English Language (Huddleston & Pullum, 2002) does not hold this view: they call it a past-participial clause functioning as a post-head modifier² in the NP structure. So, an NP can have any of these four types of clause as a post-head modifier:

i. Where's the book I lent you? [relative]
ii Kim is the person to do the job. [infinitival]
iii People living near the site will be seriously disavantaged. [gerund-participial]
iv She came across some letters written by her grandmother. [past-participial]

In short, neither your teacher nor your friend is wrong. These are two different analyses that will come up the same conclusion. Just like math: 3+3 equals 6, and so does 2+4 :).

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¹ I find it more logical to say that the relativized element is "kind of number", which is singular.
² Note that CGEL calls it a clause, not a phrase.

Answer 2

People will buy the classics based on her recommendation but sales won't reach the kind of numbers [achieved in the first book club].

The bracketed element does modify "kind of numbers", but it is a past-participial clause, not a relative one.

It has a similar meaning to the relative clause which were achieved in the first book club, but I'd avoid calling a relative clause since there is no possibility of it containing a relative phrase (cf. * ... but sales won't reach the kind of numbers which achieved in the first book club).

Note that the crucial property of a relative clause is that it must contain an element - actually present or understood - that is anaphorically related to an antecedent. This is the basis for the term 'relative clause', and likewise relative pronoun.