I recently had a problem with my MacBook Air. I went to Apple and they said they would fix it but all my data will get deleted. I said okay but when I got my MacBook back, I didn't know my apps would get deleted. Some of they apps were iMovie, Pages and Numbers. They were already installed when I first got the MacBook.
Well, when they say "all your data will get deleted" that means apps too.
You can go to the Mac App Store, click on the Purchases tab, and re-install your apps.
unfortunately, your apps are gone, or their saved date is. You can go to the app store's purchased section, and re-download those apps. Its advised to always make periodic backups of your computers Harddrive, so if something goes wrong, you wont lose much.
If you are running a new version of OS X, say El Capitan, you may have ICloud Drive, pages will automatically upload to your iCloud drive, you could check that, I have never used iMovie, but their is a possibility that it may also do as pages does.