I want to know the standard procedure and type of exams (if any) that
American Express uses to evaluate candidates that are interested in
working for the company.

I expect the answer you give me to help me understand the standard
procedure and prepare for such exams if necessary. In other words, the
answer you give should indicate weather the process is based purely on
psychological evaluations, or if quantitative thinking is also
evaluated and how.

fwiw I took the personality profile test for Amex Financial Advisors
in Tampa in 1998 or so.  It was entirely a psychological profile test
for NASD registered reps.  There would have been no way to prepare. 
Some makers of the profile tests also say that they can tell when you
are just giving the answers that you think they want to hear - ie
outgoing salesperson type.  Good luck to you.

I was hired by the American Express Co, in Mexico City in 1999. I'll
start by saying That AMEX has a worldwide policy of filling every open
position, whenever possible, with its own employees. All vacants are
posted and available to see for all the employees around the world. If
the vacant can't be filled after a certain time with internal
candidates (which has to be duly explained by the hirng person), then
they turn to external candidates. In my case, I was contacted by AMEX
by a Human Resources consultant (head hunter) and the process to get
hired took about a month from the day they contacted me for the first
time, until they made me an offer to stay. I was first interviewed by
the head hunter, then I had one interview with the human resources
manager of AMEX in Mexico. The third interview was with the peson who
was going to be my boss, then I had 2 additional interviews with 2
directors to whom I would be very related , given the nature of my
job. Finally, I had to spend half a day with them doing some tests.
These were competence tests, where I had to answer what would be my
approach to solving certain problems. The hypotetical problems
presnted to me to be "solved" were from different natures and were
supposed to measure my abilities in different fields: finance,
marketing, administration, relation with fellow workers, relation with
top management, relation with subordinates, etc. There were not right
or wrong answers to each question, but the whole set of questions gave
AMEX a broad view of who I was, what was my approach to solve problems
and how was my management style. As I said, I was hired shortly after
that. Can't tell if the tests test are the same for every position and
in every country, my guess is that tests are actually different in
every case. There was no way for me to prepare  for this kind of test,
I just had to use good judgement, use my experience and be as honest
as I could. Hope this helps and good luck.

Sam