A woman with offensive stools and easy bruising likely has a deficiency in which vitamin?

The symptoms presented—a combination of offensive stools and easy bruising—suggest a deficiency in Vitamin K. This vitamin is crucial for the synthesis of several clotting factors in the liver, including factors II, VII, IX, and X. A deficiency can lead to coagulopathy, which manifests as easy bruising and bleeding tendencies due to impaired blood clotting.

Offensive stools can also be associated with malabsorption issues, which can occur in conditions that disrupt the absorption of fat-soluble vitamins like Vitamin K. These fat-soluble vitamins are typically absorbed in the intestines alongside dietary fats, and any impairment in this process can lead to deficiencies.

The other vitamins listed do not directly correlate with the combination of symptoms: Vitamin A is primarily involved in vision and immune function; Vitamin B12 is crucial for red blood cell production and neurological function; Vitamin D is important for calcium metabolism and bone health. None of these directly lead to the coagulopathy indicated by the bruising or the malabsorption suggested by the offensive stools. Therefore, the presence of easy bruising and malabsorption of nutrients points strongly toward a deficiency in Vitamin K.