Which two conditions could present with purulent nasal discharge?

Purulent nasal discharge is often associated with infections, particularly those caused by bacteria. The presence of pus indicates that the body is fighting an infection, which can result from conditions like bacterial sinusitis and bacterial rhinitis.

Bacterial sinusitis typically leads to inflammation of the sinus cavities where thick, yellow or green pus-filled discharge is common due to the accumulation of bacteria, mucus, and inflammatory cells. Similarly, bacterial rhinitis, which is an infection of the nasal lining, can also produce purulent discharge. Both conditions involve the nasal passages and are characterized by the thick, colored discharge that indicates a bacterial infection.

The other conditions listed do not typically present with purulent discharge. Allergic rhinitis and nasal polyps tend to result in clear or watery discharge due to allergic processes rather than bacterial infection. Viral rhinopharyngitis also generally leads to clear nasal discharge, while the term "hay fever" refers to allergic rhinitis, which is not associated with purulent discharge but rather with watery and itchy symptoms. Chronic sinusitis may involve purulent discharge, but it is more commonly associated with prolonged inflammation rather than acute bacterial infection, thus making B the most fitting answer.