Final answer:
External bleeding would be most difficult to control in the case of a Carotid artery laceration, especially with low blood pressure, due to the artery's vital role and proximity to the brain.
Step-by-step explanation:
The situation in which external bleeding would be MOST difficult to control is A) Carotid artery laceration, BP 70/50 mmHg. The carotid artery is a major artery that supplies the brain with oxygenated blood. A laceration here, combined with low blood pressure, signifies a reduced perfusion to the brain and could quickly lead to hypoxia or ischemia, creating an urgent medical emergency. The body's hemostatic mechanisms may not be able to control the hemorrhage effectively. High blood pressure, as seen in option B) Femoral artery laceration, BP 140/90 mmHg, could exacerbate bleeding, but the carotid artery's critical role and the seriousness of its laceration outweigh the increased pressure factor.