**Core Concept**
Truncus arteriosus is a congenital heart defect characterized by a single blood vessel arising from the heart, which then divides into the pulmonary artery and aorta. This defect leads to severe cyanosis due to the mixing of oxygenated and deoxygenated blood. Ballooned atrial septostomy, also known as the Rashkind procedure, is a palliative treatment that creates a shunt between the atria to improve oxygenation.

**Why the Correct Answer is Right**
The administration of Prostaglandin E is essential in this scenario as it helps to keep the ductus arteriosus open, which is a vital shunt for the infant's survival. The Rashkind procedure was then performed to create an atrial septal defect, allowing blood to shunt from the left to the right atrium and improving oxygenation. This is a classic diagnostic and therapeutic approach for truncus arteriosus, as the infant's cyanosis is a result of the mixing of oxygenated and deoxygenated blood.

**Why Each Wrong Option is Incorrect**
**Option A:** This is not relevant to the scenario described, as it does not involve the administration of Prostaglandin E or the Rashkind procedure.

**Option B:** Tetralogy of Fallot is a different congenital heart defect characterized by four components: ventricular septal defect, pulmonary stenosis, right ventricular hypertrophy, and an overriding aorta. While it can also cause cyanosis, the treatment approach is different, and the Rashkind procedure is not typically used.

**Option C:** Transposition of the great arteries is another congenital heart defect where the aorta arises from the right ventricle and the pulmonary artery from the left ventricle. The treatment involves a different approach, typically with a balloon atrial septostomy followed by surgical correction.

**Option D:** Hypoplastic left heart syndrome is a complex congenital heart defect where the left side of the heart is underdeveloped. While it can cause cyanosis, the treatment approach is different, and the Rashkind procedure is not typically used.

**Clinical Pearl / High-Yield Fact**
The Rashkind procedure is a palliative treatment for certain congenital heart defects, and the administration of Prostaglandin E is crucial in maintaining the patency of the ductus arteriosus in these infants.

**Correct Answer: C.** Transposition of the great arteries.