To extend the shelf life of your apples it is advisable to refrigerate them immediately. For long term storage we keep our refrigeration room close to 32 degrees Fahrenheit. This is generally colder than most household refrigerators and while it is at, or close to freezing, the natural sugars in the apples lower their freezing point thereby keeping them from freezing and spoiling. For lots of great information about storing fruits and vegetables check out this document from Washington State University.
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