## **Core Concept**
The question describes a patient with symptoms of pneumonia, and the sputum examination reveals a gram-positive, partially acid-fast bacterium with branching filaments that grows on sheep blood agar. This points towards an infection caused by a specific type of bacteria that has distinctive characteristics.

## **Why the Correct Answer is Right**
The correct answer, *Nocardia*, is a gram-positive, partially acid-fast bacterium that forms branching filaments. *Nocardia* species are known to cause nocardiosis, which can manifest as pneumonia, especially in immunocompromised individuals. They are characterized by their ability to grow on routine media like sheep blood agar and are partially acid-fast due to the presence of mycolic acids in their cell walls. This matches the description provided in the question.

## **Why Each Wrong Option is Incorrect**
- **Option A:** *Streptomyces* are also gram-positive, filamentous bacteria but are typically not pathogenic to humans and do not match the clinical presentation of causing pneumonia.
- **Option B:** *Actinomyces* are gram-positive, filamentous bacteria that are anaerobic and do not grow on sheep blood agar in the presence of oxygen; they also do not exhibit partial acid-fastness.
- **Option D:** *Mycobacterium* species are acid-fast but are not gram-positive and do not typically form branching filaments.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that *Nocardia* infections are more common in immunocompromised patients and can cause a range of diseases including pulmonary nocardiosis, which presents with symptoms like fever, cough, and weight loss. The partial acid-fast property helps in differentiating *Nocardia* from other filamentous bacteria.

## **Correct Answer:** C. Nocardia.