Why "get down to" and not "get through with"?

[Asia]

English Language Tests, Intermediate level

ESL/EFL Test #163 "Idioms with the phrasal verb get", question 1

After the small talk was over, it was time for the two heads of state to ......... discussions concerning bilateral relations between the two countries.

(a) get through with
(b) get by with
(c) get down to
(d) get around

English Language Tests, Intermediate level

ESL/EFL Test #163 "Idioms with the phrasal verb get", answer 1

After the small talk was over, it was time for the two heads of state to get down to discussions concerning bilateral relations between the two countries.

Correct answer: (c) get down to

Your answer was: incorrect
After the small talk was over, it was time for the two heads of state to get through with discussions concerning bilateral relations between the two countries.
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Why "get down to" and not "get through with"?

Asia

[Mister Micawber]

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Get down to = begin. Get through with = finish. Small talk is how we begin a meeting, so that in this sentence, the serious discussions had not yet begun.
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Native English teacher at Mister Micawber's