Final answer:
When a patient with diabetes insipidus responds positively to administered ADH, it indicates central (neurogenic) diabetes insipidus because it shows that the kidneys can respond to the hormone.
Step-by-step explanation:
If a patient with diabetes insipidus responds to the administration of antidiuretic hormone (ADH), the correct interpretation of the response is that the disorder is central (neurogenic) diabetes insipidus. This form of the condition occurs when the posterior pituitary does not secrete enough ADH, which is essential for water reabsorption by the kidneys. An effective response to administered ADH indicates that the kidneys are capable of responding to the hormone, thus excluding nephrogenic diabetes insipidus, where the kidneys are not responsive to ADH.