Final answer:
A Martini should be shaken vigorously for about 10 to 15 seconds, not by counting shakes, to chill it sufficiently without over dilution, which is based on bartending technique and personal preference.
Step-by-step explanation:
The question of how many times a Martini should be shaken is not strictly a matter of fact, but rather it falls into the realm of bartending techniques and personal preference. There is no definitive answer to this question. However, conventional wisdom among professional bartenders suggests that shaking a Martini vigorously for about 10 to 15 seconds is ample to ensure that it is sufficiently chilled without being overly diluted.
Shaking a drink can break up the ice and add more water to the drink, which can result in dilution. Therefore, the options provided (3, 5, 7, 10 times) do not precisely represent the typical bartending practice. A well-chilled Martini is usually achieved by a consistent and vigorous shake rather than counting the number of shakes.