Step 1: Identify the clinical picture. An elderly man with chest pain and productive cough whose sputum grows gram-positive cocci on blood agar points strongly to Streptococcus pneumoniae (pneumococcus), the commonest cause of community-acquired lobar pneumonia.
Step 2: On blood agar pneumococcus shows alpha (green) haemolysis with draughtsman or carrom-coin colonies that are autolytic. The task is to confirm pneumococcus and separate it from viridans streptococci, which are also alpha-haemolytic gram-positive cocci.
Step 3: The two tests that distinguish pneumococcus from viridans streptococci are bile solubility and optochin sensitivity. Pneumococcus is bile soluble (its autolytic enzyme is activated by bile salts) and optochin sensitive; viridans streptococci are bile insoluble and optochin resistant.
Step 4: Evaluating the distractors: catalase is negative for all streptococci and only separates staphylococci from streptococci, so it cannot identify pneumococcus specifically. Bacitracin sensitivity is used for group A Streptococcus pyogenes, not pneumococcus. Oxidase is used for gram-negative organisms such as Pseudomonas and Neisseria.
Step 5: Therefore the most useful confirmatory test here is bile solubility, option A.