Management depends on the size, of course. But the data points at no specific critical numbers. The histogram of firms by the number of employees:
(hat tip to Jeffrey Groen at the BLS for the data)
And the log scale:
If ten or any other number had any significance, we'd see abnormal behavior around it. Management experiences transitional difficulties and some firms disappear. It would look like discontinuities or multiple peaks, as with the middle income trap. But the distribution does not support this claim. Perhaps, specific numbers matters for certain subpopulations of firms, for instance, the IT industry. In that case, it'd be interesting to look at the data. But until that it would be overall great if authors were more responsible and back their statements with minimal evidences.