**Core Concept**
The patient's symptoms of rapid onset hirsutism and amenorrhea are suggestive of a hormonal imbalance, specifically an excess of androgens. This condition is often associated with polycystic ovary syndrome (PCOS) but can also be caused by other endocrine disorders.

**Why the Correct Answer is Right**
The best investigation for this patient is a pelvic ultrasound to evaluate the ovaries for any abnormalities. PCOS is characterized by multiple small cysts on the ovaries, but other causes of androgen excess, such as congenital adrenal hyperplasia or a tumor, may also be identified through ultrasound. The pelvic ultrasound can provide valuable information about the size and appearance of the ovaries, helping to guide further diagnostic testing and treatment.

**Why Each Wrong Option is Incorrect**
**Option A:** Serum androgen levels may be elevated in patients with hirsutism, but measuring androgen levels alone is not sufficient to diagnose the underlying cause of the patient's symptoms. It may also not provide information about the ovaries.
**Option B:** A CT scan of the abdomen may be useful in identifying larger ovarian tumors or adrenal masses, but it is not the best initial investigation for a patient with suspected PCOS or other hormonal imbalances.
**Option C:** A bone age x-ray may be useful in patients with suspected precocious puberty, but it is not relevant to the diagnosis of hirsutism and amenorrhea in a 16-year-old girl.

**Clinical Pearl / High-Yield Fact**
In patients with suspected PCOS, a pelvic ultrasound can help identify the presence of multiple small ovarian cysts and guide further diagnostic testing and treatment.

**Correct Answer: C. CT scan of the abdomen.**