Which system variable controls the size of the table cache?

table_cache: This is the correct option. The table_cache system variable in MySQL controls the size of the table cache. It determines the maximum number of open tables that MySQL keeps cached in memory for quick access.
cache_table: This option is incorrect. "cache_table" is not a recognized system variable in MySQL for controlling the size of the table cache.
open_cache: This option is incorrect. "open_cache" is not a recognized system variable in MySQL for controlling the size of the table cache.
cache_open: This option is incorrect. "cache_open" is not a recognized system variable in MySQL for controlling the size of the table cache.

Therefore, the system variable that controls the size of the table cache in MySQL is Option A: table_cache.