**Core Concept**
The patient's family history of ovarian carcinoma, combined with a firm breast mass, raises the suspicion of a genetic predisposition to breast and ovarian cancer. This scenario suggests a possible mutation in the BRCA1 or BRCA2 genes, which are tumor suppressor genes that play a crucial role in maintaining genomic stability.

**Why the Correct Answer is Right**
The correct answer is BRCA1/BRCA2 genetic testing. This test assesses for mutations in the BRCA1 and BRCA2 genes, which are associated with an increased risk of breast and ovarian cancer. Patients with a family history of ovarian carcinoma, particularly at a young age, are more likely to have a BRCA1 or BRCA2 mutation. Genetic testing can identify these mutations, allowing for targeted surveillance, risk-reducing measures, and early detection of cancer.

**Why Each Wrong Option is Incorrect**
* **Option A:** CA 15-3 and CA 27-29 are tumor markers used for monitoring breast cancer, but they are not used for assessing genetic mutations.
* **Option B:** Mammography and ultrasound are imaging modalities used for breast cancer screening, but they do not assess for genetic mutations.
* **Option C:** MRI is a sensitive imaging modality for breast cancer screening, but it does not assess for genetic mutations.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with a family history of ovarian carcinoma, it's essential to consider genetic testing for BRCA1 and BRCA2 mutations, as these mutations significantly increase the risk of breast and ovarian cancer.

**Correct Answer:** C. MRI