Final answer:
Patient A is most likely to have hypothyroidism, while Patient B is most likely to have hyperthyroidism based on their symptoms.
Step-by-step explanation:
Patient A's symptoms of weight gain, cold sensitivity, low heart rate, and fatigue are consistent with hypothyroidism. Hypothyroidism is a condition in which the thyroid gland is underactive, resulting in a decreased metabolic rate and a variety of symptoms including weight gain and fatigue.
Patient B's symptoms of weight loss, profuse sweating, increased heart rate, and difficulty sleeping are consistent with hyperthyroidism. Hyperthyroidism is a condition in which the thyroid gland is overactive, leading to an increased metabolic rate and a variety of symptoms including weight loss and increased heart rate.
Based on the symptoms described, Patient A is most likely to have hypothyroidism, while Patient B is most likely to have hyperthyroidism.