How to find out files created within a date range, and above a certain size

Looking at the regular weekly backups, I saw a jump in size that was not accounted for by regular normal growth.

ls -ltrh /backupdirectory
...
-rw-r--r-- 1 root root 31G May 25 03:23 backup-2014-05-25.dump
-rw-r--r-- 1 root root 31G Jun 1 03:22 backup-2014-06-01.dump
-rw-r--r-- 1 root root 32G Jul 6 03:21 backup-2014-07-06.dump
-rw-r--r-- 1 root root 41G Aug 3 03:25 backup-2014-08-03.dump
...

I needed to find out which files caused this big jump, so I used this command, which finds out files created (actually, modified) within a time frame, and larger than a certain threshold (more than 10 MB in size in this case):

find / -newermt "2014-07-06" ! -newermt "2014-08-03" -size +10M -exec ls -lh {} \;

The results were virtualized disk images. So nothing sinister. Once I pruned those back to what is actually being used, I saved myself several gigabytes of backup storage space.