I was ____ the point of giving up on them when they arrived.
the right answer," at the point" ????
Is there more bristish people, then americans that go on this site?
I would suggest there are more Americans than British visitors here. I chose "at" ('British' English) simply because I didn't like the sound of the repeated "on". Normally I probably would have chosen "on" though.
Perhaps it's best to do a quick mental division to see the ratio between British on/at and American on/at. Seems a larger percentage of Brits find it acceptable to use on as a substitute for at. Personally an 'at' person myself (British).