**Core Concept**
The question is testing the knowledge of a specific vitamin deficiency that leads to a range of symptoms including glossitis, dementia, skin changes, and gastrointestinal symptoms. This deficiency is related to a critical coenzyme required for various metabolic processes.

**Why the Correct Answer is Right**
The correct answer is related to Biotin deficiency. Biotin is a B-complex vitamin that serves as a coenzyme for carboxylation reactions, including the synthesis of fatty acids and amino acids. Deficiency of biotin can lead to a range of symptoms including glossitis, dermatitis, and neurological symptoms such as dementia. The skin manifestations are characterized by rough, keratotic areas due to impaired keratinization. Gastrointestinal symptoms such as diarrhea and abdominal pain are also common.

**Why Each Wrong Option is Incorrect**
* **Option A:** Thiamine (Vitamin B1) deficiency causes beriberi and Wernicke-Korsakoff syndrome, but not the specific combination of symptoms mentioned in the question.
* **Option B:** Niacin (Vitamin B3) deficiency causes pellagra, which is characterized by dermatitis, diarrhea, and dementia, but the skin changes are typically described as "three Ds": diarrhea, dermatitis, and dementia.
* **Option C:** Folate deficiency can cause megaloblastic anemia, but it does not typically cause glossitis, skin changes, or dementia.

**Clinical Pearl / High-Yield Fact**
Biotin deficiency can be caused by a diet lacking in biotin-rich foods, such as nuts and leafy greens, as well as by certain medications, including anticonvulsants and isoniazid.

**Correct Answer: C. Biotin deficiency.**