Which diagnostic study is recommended to definitively diagnose a painless, mobile breast mass in a 35-year-old woman?

A core-needle biopsy is the recommended diagnostic study for definitively diagnosing a painless, mobile breast mass in this scenario because it allows for the extraction of a larger tissue sample compared to fine-needle aspiration. This larger sample size increases the likelihood of obtaining sufficient material for accurate histopathological evaluation, which is crucial for distinguishing between benign and malignant conditions.

In the case of a breast mass, especially in a woman under 40, it is important to ensure the diagnosis is accurate, as breast cancer is less common but still a possibility. While fine-needle aspiration can provide quick results and is less invasive, its smaller sample size may not provide enough information for a definitive diagnosis, especially if the cellular characteristics are not clear.

Other imaging studies like mammograms and ultrasounds can be useful in evaluating breast masses, particularly for assessing the characteristics of the mass and helping to guide the choice of further diagnostic procedures. However, they do not provide the definitive tissue diagnosis that a biopsy does. In conclusion, a core-needle biopsy offers a balanced approach, combining the need for a significant tissue sample while still being performed percutaneously.