**Core Concept:** Familial cancer syndromes are inherited disorders characterized by an increased risk of developing multiple types of cancer. These syndromes are caused by mutations in specific genes, leading to abnormal cell growth and tumor development. In this case, the woman's mother died of endometrial cancer and her brother has colon cancer, suggesting a predisposition to a familial cancer syndrome.

**Why the Correct Answer is Right:** The correct answer is **D** - **BRCA1**. BRCA1 is a tumor suppressor gene that plays a crucial role in maintaining genomic stability, regulating cell cycle, and preventing DNA damage. Mutations in BRCA1 can lead to breast and ovarian cancer, as well as endometrial cancer in females.

In this case, the family history demonstrates a strong association with breast and endometrial cancer, making BRCA1 the most likely gene to be mutated.

**Why Each Wrong Option is Incorrect:**

**A.** BRCA2 (Breast Cancer 1) is another tumor suppressor gene, but it is less commonly associated with endometrial cancer compared to BRCA1.

**B.** Lynch syndrome (HNPCC) is a familial cancer syndrome mainly associated with colon, endometrial, and ovarian cancer. However, the patient has colon cancer and her mother had endometrial cancer, not the other way around.

**C.** TP53 (tumor protein p53) is another tumor suppressor gene associated with various types of cancer. However, the family history does not specifically demonstrate a strong association with endometrial cancer.

**E.** Li-Fraumeni syndrome is an autosomal dominant disorder associated with breast, bone, brain, and soft tissue sarcoma cancers. The family history does not clearly point towards this syndrome.

**Clinical Pearl:**

Inherited mutations in BRCA1 or BRCA2 genes increase the risk of breast, ovarian, and endometrial cancers. Family history plays a crucial role in identifying the potential genetic predisposition, as demonstrated by the patient's mother's and brother's cancer history. However, the family history demonstrates a strong association with breast and endometrial cancers, making BRCA1 the most likely gene to be mutated.

**Correct Answer Explanation:** The correct answer is D. In this case, the family history demonstrates a strong association with breast and endometrial cancers, making BRCA1 the most likely gene to be mutated. The patient's mother had endometrial cancer, which aligns more with a BRCA1 mutation, compared to other options like BRCA2, Lynch syndrome, Li-Fraumeni syndrome, or TP53. While the patient has colon cancer, the family history does not specifically demonstrate a strong association with endometrial cancer, making other options less likely.