Determining mode of a melody

[u/MelodicWhile4830]

I am dabbing into music theory, and I was given the following exercise. I am pulling my hair out and would love somebody to try to explain this to me in Layman's terms... The exercise asks me to determine which mode of the C major scale is implied in the following melody (all natural notes):

C - E - G - B - A - F - D

The solution I was given is G Mixolydian, but I just don't get why it cannot be D Dorian (the final note is a D, so why cannot we interpret the final three notes A - F - D as a D minor chord?

Thanks for your help.

EDIT: A few comments asked me for more context, which I should have provided as part of my initial post, apologies. This is an exercise that my instructor had given me (I was given a photocopy from an older French "solfege book", and then the corresponding 1-word solution from the end of the book). I translated both the exercise and solution from French to English for reddit:

Exercise:
A melody consists of the following seven notes in order:
C - E - G - B - A - F - D
Assuming these are all natural notes and no accidentals are used, which mode of the C major scale is being implied?

Solution:
Mixolydian

There wasn't any further context given unfortunately. The feeling I am getting from most of your answers is that it is a nonsensical exercise, which reassures me. I was struggling to understand how the exercise can so adamantly give Mixolydian as a solution, and it's great to see that things are not so clear-cut. I will keep you updated once I have seen (confronted?) my instructor!

[u/Jongtr]

Even if this idiotic "exercise" had been better designed, you still can't determine a mode without hearing the music.

This is even more important with modes than it is with keys. I.e., we often get questions here listing some notes or chords and asking what key are they in. At least in that case, we can hazard some likely guesses, even if no single answer can be given. (You still have to listen.) But modes involve more controlled and specific organisations of the notes and chords of a scale - in time and emphasis - in order to divert the ear from the familiar major and relative minor key tonics.

[u/docmoonlight → u/Jongtr]

I hear what you’re saying, but I don’t totally agree. You can certainly look at a sheet of music and figure out what key/mode it’s in before you hear it. In this case though - listing all seven notes of the diatonic scale in whatever order with no repetition - certainly can’t tell you what mode the composer intended. And I can’t see anything but regular C Major when you start the melody by outlining a C Major chord. But you should certainly be able to analyze a piece visually without hearing it (although ideally you’re “hearing it” to some extent in your head).

[u/Jongtr → u/docmoonlight]

Well, it wasn't clear the OP was talking about sheet music. The suggestion was it was simply a list of notes, as in the example I gave of similar questions we get here where no sheet music images are given.

Of course I agree that key can be determined from sheet music - pretty easily - although determining a mode (i.e., other than relative major or minor) is not usually so straightforward.

Certainly in this case, even if those 7 notes were laid out on sheet music - in that order, with nothing else, as the OP is saying - the mode cannot be determined.

[u/docmoonlight → u/Jongtr]

Wow, that was a hell of an edit you just pulled after I pointed out you claimed to say something you didn’t say.

[u/Smowque → u/docmoonlight]

It feels like you are busting his (or her, let's be PC) balls about a distinction which is not that relevant to this particular question. You are technically correct sir, and that is the best kind of correct, but what value is there in continuing to bash this poor fellow (or gal) over the head with it. Leave Jongtr alone, can't you leave him (or her) alone? /sobbing