**Core Concept**
Primary amenorrhea in a child can be caused by various factors, including hormonal imbalances, anatomical abnormalities, or genetic disorders. The progesterone challenge test and combined progesterone and estrogen test are used to evaluate the functional status of the hypothalamic-pituitary-ovarian axis.

**Why the Correct Answer is Right**
The positive combined progesterone and estrogen test suggests that the child has a functional uterus and ovaries, as estrogen is essential for endometrial proliferation and progesterone for secretory changes. This test helps rule out conditions such as vaginal agenesis or testicular feminization syndrome. The negative progesterone challenge test, however, indicates that the child's ovaries are not responding to progesterone, which is necessary for secretory changes in the endometrium.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not provided, but we can infer that it might be a distractor related to anatomical abnormalities like vaginal agenesis or imperforate hymen. However, the positive combined test makes this option less likely.
* **Option B:** This option might be related to conditions like premature ovarian failure or ovarian failure due to chemotherapy. However, the child's age and the positive combined test make this option less likely.
* **Option C:** This option might be related to conditions like polycystic ovary syndrome (PCOS) or other forms of hyperandrogenism. However, the negative progesterone challenge test and positive combined test do not support this diagnosis.

**Clinical Pearl / High-Yield Fact**
In cases of primary amenorrhea, it is essential to perform a thorough history, physical examination, and laboratory tests to identify the underlying cause. The combined progesterone and estrogen test can help differentiate between conditions with and without functional ovaries.

**Correct Answer:** C. Hypogonadotropic hypogonadism, such as Kallmann syndrome.