最後の質問が解けたところで、試験終了のチャイムが鳴ったんだ。
What does で after ところ mean ?
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Sign up to join this communityOne of the definitions of ところで is 「時に(ときに)」 'at the time of ____', 'as _____ happens/happened'.
'As I solved the last question, the bell ending the test sounded.'
It is the 連用形{れんようけい} conjugation form of the auxiliary だ, ( the auxiliary だ denotes assert/conclude something ), here what is omitted after で is
最後の質問が解けたところであった時、試験終了のチャイムが鳴ったんだ。
Meaning,
When it was the time I finished the last question, the bell rang to let the test takers to know it was a finish time.