What diagnosis is indicated by weight gain, a deep voice, and dry skin?

The symptoms of weight gain, a deep voice, and dry skin are indicative of hypothyroidism. In hypothyroidism, the thyroid gland is underactive and does not produce enough thyroid hormones, which play a crucial role in regulating metabolism. This deficiency can lead to various systemic effects.

Weight gain occurs because a slower metabolism can cause an increase in body weight. The thyroid hormone helps regulate energy expenditure, so when it's low, metabolism slows down, leading to weight gain despite a normal or reduced caloric intake.

A deep voice can be attributed to the accumulation of mucopolysaccharides and changes in the larynx associated with lower thyroid hormone levels. Additionally, dry skin is a common symptom because thyroid hormones are essential for maintaining skin health; a deficiency leads to dryness, flakiness, and other skin issues.

The other options do not align with the combination of symptoms provided. Hyperthyroidism, for instance, typically presents with weight loss and increased sweating, while Cushing's syndrome is characterized by specific patterns of obesity and skin changes, and amyloidosis involves more complex systemic symptoms that do not primarily include the three described here. Thus, hypothyroidism aligns well with the given symptoms.