What’s the most effective way to back-up / save data on Oracle 11g large data sets

The logic with 'A' and 'B' might be "hidden" behind a virtual column on which you could do the partitioning:

alter session set nls_date_format = 'yyyy-mm-dd';
drop   table tq84_partitioned_table;

create table tq84_partitioned_table (
  status varchar2(1)          not null check (status in ('A', 'B')),
  date_a          date        not null,
  date_b          date        not null,
  date_too_old    date as
                       (  case status
                                 when 'A' then add_months(date_a, -7*12)
                                 when 'B' then            date_b
                                 end
                        ) virtual,
  data            varchar2(100) 
)
partition   by range  (date_too_old) 
( 
  partition p_before_2000_10 values less than (date '2000-10-01'),
  partition p_before_2000_11 values less than (date '2000-11-01'),
  partition p_before_2000_12 values less than (date '2000-12-01'),
  --
  partition p_before_2001_01 values less than (date '2001-01-01'),
  partition p_before_2001_02 values less than (date '2001-02-01'),
  partition p_before_2001_03 values less than (date '2001-03-01'),
  partition p_before_2001_04 values less than (date '2001-04-01'),
  partition p_before_2001_05 values less than (date '2001-05-01'),
  partition p_before_2001_06 values less than (date '2001-06-01'),
  -- and so on and so forth..
  partition p_ values less than (maxvalue)
);

insert into tq84_partitioned_table (status, date_a, date_b, data) values 
('B', date '2008-04-14', date '2000-05-17', 
 'B and 2000-05-17 is older than 10 yrs, must be deleted');


insert into tq84_partitioned_table (status, date_a, date_b, data) values 
('B', date '1999-09-19', date '2004-02-12', 
 'B and 2004-02-12 is younger than 10 yrs, must be kept');


insert into tq84_partitioned_table (status, date_a, date_b, data) values 
('A', date '2000-06-16', date '2010-01-01', 
 'A and 2000-06-16 is older than 3 yrs, must be deleted');


insert into tq84_partitioned_table (status, date_a, date_b, data) values 
('A', date '2009-06-09', date '1999-08-28', 
 'A and 2009-06-09 is younger than 3 yrs, must be kept');

select * from tq84_partitioned_table order by date_too_old;

-- drop partitions older than 10 or 3 years, respectively:

alter table tq84_partitioned_table drop partition p_before_2000_10;
alter table tq84_partitioned_table drop partition p_before_2000_11;
alter table tq84_partitioned_table drop partition p2000_12;

select * from tq84_partitioned_table order by date_too_old;

You will have to examine how the question is worded. By default 11g will create all three tablespaces. You can however create a database with only SYSTEM and SYSAUX. Technically speaking you can upgrade pre-10g database and not add SYSAUX, or remove the SYSAUX tablespace after the database is created and therefore have a database with only a SYSTEM tablespace, but you would be ill advised to do so and I really don't think they would look for that in an answer.

From the 11.2 Administration Guide:

The SYSAUX tablespace is always created at database creation.

From another section of the Administration Guide:

An auto-extending undo tablespace named UNDOTBS1 is automatically created when you create the database with Database Configuration Assistant (DBCA)...

If no undo tablespace is available, then the instance starts without an undo tablespace, and undo data is written to the SYSTEM tablespace. You should avoid running in this mode.

From the 10.2 Concepts Guide:

...the SYSAUX tablespace is always created during database creation or database upgrade...

During normal database operation, the Oracle database server does not allow the SYSAUX tablespace to be dropped or renamed. Transportable tablespaces for SYSAUX is not supported.

Note: If the SYSAUX tablespace is unavailable, such as due to a media failure, then some database features might fail.

From the 10.1 SQL Reference:

You cannot drop the SYSTEM tablespace. You can drop the SYSAUX tablespace only if you have the SYSDBA system privilege and you have started the database in MIGRATE mode.

From the 10.1 Administrators Guide:

If the SYSAUX tablespace becomes unavailable, core database functionality will remain operational. The database features that use the SYSAUX tablespace could fail, or function with limited capability.

http://oradbpedia.com/wiki/The_SYSAUX_Tablespace has this take:

The SYSAUX tablespace is a new tablespace that is required in Oracle Database 10g...

When you migrate to Oracle Database 10g, the SYSAUX tablespace needs to be created as a part of that migration. This is done after mounting the database under the new Oracle Database 10g database software. Once you have mounted it, open the database in migrate mode with the startup migrate command. After the database is open, you can create the SYSAUX tablespace.

Note: The loss of the SYSAUX tablespace is not fatal to your database. In our testing it appears that the only real impact is that certain functionality related to the occupants of the SYSAUX tablespace is lost.

Earlier versions did not have a SYSAUX tablespace:

SYSAUX is the name of the compulsory tablespace, introduced in Oracle 10g.