Adding asc/desc arrows next to dropdown

We have a sort selection dropdown list with around 6 options. We'd like the user to be able to specify the direction of the sort. Is adding up/down arrows like this intuitive?

In looking at other sites, it's common to see the sort direction within the options themselves (e.g., "Price (lowest to highest)", "Price (highest to lowest)", etc.)

But we have a number of different quantities in our case and fear the drop-down would become too cluttered if each one was duplicated like that.