possible_keys exist but key is NULL

[David McLaughlin]

Kind of new here. Your patience is appreciated.

I'm doing something of the sort:

mysql> CREATE TABLE `test` ( `a` INT KEY, `b` INT, `c` INT );
mysql> CREATE INDEX `my_index` on `test` ( `b`, `c` );
mysql> INSERT INTO `test` (`b`, `c` ) VALUES( 1223, 123 );
mysql> EXPLAIN SELECT * FROM `test` WHERE `b` > 50 AND `c` > 100;
+----+-------------+-------+--------+---------------+------+---------+------+------+-------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+--------+---------------+------+---------+------+------+-------+
| 1 | SIMPLE | test | system | my_index | NULL | NULL | NULL | 1 | |
+----+-------------+-------+--------+---------------+------+---------+------+------+-------+
1 row in set (0.00 sec)

Of course, my real tables have millions of rows, etc.

The problem is there is a "possible_key" but no key is chosen.
I can force the key choice using FORCE INDEX (and the query becomes efficient), but I don't want to "force" all my database programs to worry about what I call my indexes and whether they need to force an index, etc.

ANALYZE TABLE doesn't help.

Any help is appreciated,
Thanks,
David McLaughlin