Seven consecutive whole numbers have an average of 34. What is the average of the three largest of them?

Seven consecutive numbers are symmetric about their middle term, so the middle one is 34 and the numbers run 31, 32, 33, 34, 35, 36, 37. The three largest are 35, 36 and 37, and being consecutive their average is the middle one, 36. 37 is the largest number, not the average of the three. 35 is the smallest of the three. 34 assumes any block taken from the set carries the same average as the whole, which fails as soon as the block sits off-centre.