**Core Concept**
The patient's symptoms, including abdominal pain, blood in stools, and a palpable mass, are suggestive of a gastrointestinal obstruction or a malignancy. A Barium Study is a radiographic examination that uses barium sulfate to visualize the gastrointestinal tract and diagnose structural abnormalities.

**Why the Correct Answer is Right**
The patient's presentation is consistent with a **meckel's diverticulum**, a congenital anomaly of the small intestine that can cause gastrointestinal bleeding, obstruction, and abdominal pain. A Barium Study can help identify the diverticulum by showing a filling defect or a pouch-like structure in the small intestine. The **barium** outlines the small intestine and highlights the diverticulum, making it visible on the radiograph.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because a **Meckel's diverticulum** is a specific type of gastrointestinal anomaly, whereas this option is too broad and could refer to any number of conditions.
* **Option B:** This option is incorrect because a **diverticulitis** is an inflammation of a diverticulum, usually in the colon, and would not typically present with a palpable mass or blood in stools.
* **Option C:** This option is incorrect because a **carcinoid tumor** is a type of neuroendocrine tumor that can cause gastrointestinal symptoms, but it would not typically present with a palpable mass or blood in stools on a Barium Study.
* **Option D:** This option is incorrect because a **appendicitis** is an inflammation of the appendix, which can cause abdominal pain and tenderness, but it would not typically present with blood in stools or a palpable mass on examination.

**Clinical Pearl / High-Yield Fact**
A Meckel's diverticulum is a congenital anomaly that can cause gastrointestinal bleeding due to the presence of ectopic gastric mucosa, which can lead to ulceration and bleeding.

**Correct Answer:** C.