A set $$S$$ contains 11 numbers. The average of the numbers in $$S$$ is 302. The average of the six smallest numbers of $$S$$ is 100 and the average of the six largest of the numbers is 300. What is the median of the numbers in $$S$$

The printed data give a total sum of $$11\cdot302=3322$$. The six smallest and six largest numbers would have sums $$600$$ and $$1800$$, so the shared median would have to satisfy $$600+1800-m=3322$$, giving $$m=-922$$, which is inconsistent with the intended question. The official solution marks this question as a bonus because it is wrong and nevertheless lists $$360$$ as the keyed value.