Copying files containing specific text in its content from a folder to other

Copying files containing specific text in its content from a folder to other

At times I have come across situation where by I have to copy all the
files containing a specific pattern in its content from a folder to other.
For ex.. DirA contains 100 files out of which there are 60 files which
contains a pattern say FOO and my requirement is to copy these 60 files
from DirA to DirB.
I typically write a small shell script to do this job and it works
properly. However I am trying to understand if there is a way to it only
using a combination of some commands and I need not write any shell
script.
Any pointer will be helpful.
Regards, Ramakant