To keep apples fresh longer you should store the apples in the refrigerator in the crisper drawer.
When storing apples in the refrigerator crisper drawer or in the refrigerator in general place the apples in separate bags such as in plastic sandwich bags or Ziploc bags.
The coolness of the refrigerator will make the apples last longer than they would last when stored out on the counter at room temperature.
When stored out on the counter or just at room temperature apples last between 7 to 14 days depending on the room temperature.
The apples will last longer when the room temperature is cooler than they would when the room temperature is hotter.