This is the 13365th most frequent Russian word.
набранными
"Набранными" means "collected" or "gathered."
In this sentence, "набранными" is used as a past passive participle and agrees in case and number with "баллами" (points). It describes the points that someone managed to accumulate or achieve.
Студенты гордились набранными баллами.
The students were proud of the points they scored.
Here, "набранными" functions as a past participle modifying "очками" (points). It refers to points acquired during the tournament.
Она была впечатлена набранными на турнире очками.
She was impressed by the points scored in the tournament.
In this example, "набранными" modifies "ответы" (answers), indicating that the responses were collected for analysis.