What variation of a Manhattan uses both dry and sweet vermouth?

The correct answer is the variation known as a Perfect Manhattan. This cocktail is distinguished by its use of equal parts dry and sweet vermouth, which creates a balanced flavor profile that incorporates the herbal notes of both types of vermouth. This approach offers a unique twist on the traditional Manhattan, which typically relies solely on sweet vermouth.

In a Classic Manhattan, only sweet vermouth is used, providing a rich and sweet character to the drink. A Dry Manhattan, on the other hand, uses only dry vermouth, which results in a drier and more crisp cocktail. The Rob Roy is a variation of the Manhattan that substitutes Scotch whisky for the standard bourbon or rye, but it does not change the vermouth proportions. Hence, the Perfect Manhattan stands out as the correct answer for this question about the use of both dry and sweet vermouth in one cocktail.