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The below sentence is a test question for 12th graders.

■ Rather than [focusing / focused] on romanticized emotions, he wrote on a number of deeper, more abstract ideas surrounding love, death, and religion.

I got the answer "focusing on" right but it seems "focused on" is possible, because I have seen so many "focused on" with 'person subject' as below examples.

❶ This is the sort of mindset that keeps Sergio Garcia from achieving greatness and prevents you from reaching your goals. You suddenly get focused on not making the big mistake rather than focused on hitting one shot at a time into the target area.

❷ Since I was always focused on computers, I thought at some point that if I had to, I probably would go into web design or something.
Do you agree with me?
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"focused on" is fine in the right grammatical context, but it doesn't fit the structure of the test sentence. Any sentence of the form "Rather than ..., he ..." has to use the -ing form of the verb. It's not specifically an issue with the verb "focus".

"Rather than saying sorry, he continued to be rude."

"Rather than catching up, he fell further behind."

"Rather than stopping and looking, he dashed straight across the road."
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You need the -ing form after rather than, and after any preposition or subordinating conjunction.

rather than deciding ...
used for measuring ...
instead of looking ...
after finding ...
while listening ...

You can have rather than without -ing when it's a contrast to something that came before, however.

The boys were bored rather than tired.
They were focused on animals rather than focused on plants.
We wanted our coffee after the meal rather than before.

CJ
Thank you for answering my thread, Mr Wordy.

But how come 145,000 sentences detected with "rather than focused" on Google?

Can't I think 'being' is omitted?

There should be much more sentences with "rather than" + "any past participle except focused."
Stenka25But how come 145,000 sentences detected with "rather than focused" on Google?
Again, there is no problem with "rather than focused" in the right context. A few random examples from Google:

  • "Artists and scanners tend to have expansive minds rather than focused minds."

  • "The Golden Rule is nice in theory, but it is self-focused, rather than focused on the person to whom you are responding."

  • "Fourth, general rather than focused skills are often still required for the initial evaluation of patients admitted acutely to hospital."
These are all OK. If you find any sentences using "rather than focused" that have the same pattern as your original example then they are incorrect (remember that there are vast amounts of faulty English on the Internet).
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Thank you for your immediate answer.
But I still cannot but think "focused" can be all right, if not more frequent than "focusing," as described in the below website.
http://www.totalgadha.com/gmat/2009/07/rather-than-vs-instead-of/
and also in the Webster's Learner's Dictionary, there isn't any saying that we should use only -ing form after 'rahter than.'

In ❺, I think 'sad' is possible, because 'being' is omitted.
And you can find 359,000 of "rather than being sad" in Google.

▸rather than
1 : in place of (something or someone) : instead of (something or someone)

❶ ▪ He writes at a table rather than a desk.
❷ ▪ Why do one thing rather than another?
❸ ▪ Rather than using dried herbs, he picked fresh ones from the garden. : and not
❹ ▪ She reacted by laughing rather than by getting upset.
❺ ▪ He was happy rather than sad.

2 -used to say what is not chosen or done because something else is chosen or done instead

❻ ▪ Rather than continue the argument, she walked away.
❼ ▪ I chose to sing rather than play an instrument.
Stenka25But I still cannot but think "focused" can be all right
In your original sentence, "focused" is definitely wrong.
Stenka25and also in the Webster's Learner's Dictionary, there isn't any saying that we should use only -ing form after 'rahter than.'
I did not say that you always have to use the "-ing" form of a verb after "rather than" (in fact, I gave you counterexamples from Google). What I said is that you have to use the "-ing" form in sentences that have the same structure as your original example. However, I now realise that this is not correct. You can also use the infinitive, as in your example ❻. Sorry about that; for some reason I just didn't think of it as I was concentrating on the difference between "focused" and "focusing".
Tthe word "being" solves the problem...
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My take:

On #5, " rather than being sad" is the proper structure. Mr Wordy and CJ already explained the finer points. With "rather" or " instead of " in the constuction, we need the gerund form of the verb, not the bare form.

❻ ▪ Rather than continuing with the argument, she walked away.
Alternatively: She walked away rather than continuing with the argument.