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I don't think you can permanently delete them but you can hide an app by sliding left on iOS.
 
You can hide them by swiping left in your purchased apps section of App Store. A "hide" button will appear. However apparently this only works for people with family sharing set up, which sucks.
 
My bad, I just tried it on my iPhone. Apparently, it only works on the iPad.

It works on the iPhone too (that is, swiping to hide with Family Sharing enabled). Tested on an iPhone 5 and 6.

It's easy to set up Family Sharing, too, and you don't need to actually share with anyone else. I only set it up so that I could hide old apps from my phone.
 
It works on the iPhone too (that is, swiping to hide with Family Sharing enabled). Tested on an iPhone 5 and 6.

It's easy to set up Family Sharing, too, and you don't need to actually share with anyone else. I only set it up so that I could hide old apps from my phone.

Cool beans!
 
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