Okay, let's tackle this question about Familial Adenomatous Polyposis (FAP). The user wants a detailed explanation for a multiple-choice question where the correct answer is an exception. First, I need to recall the core concepts of FAP.

FAP is an autosomal dominant condition caused by mutations in the APC gene. It's characterized by hundreds to thousands of adenomatous polyps in the colon and rectum, which almost always progress to cancer if not removed. The core concept here is the genetic basis and the risk of malignancy.

Now, the question asks which statement is not true. The correct answer is the exception. Let's think about common statements associated with FAP. For example, it's known to have extracolonic manifestations like desmoid tumors, osteomas, and congenital hypertrophy of the retinal pigment epithelium (CHRPE). Also, it's managed with colectomy, and the age of onset is typically in the second decade.

The options are not provided, but the correct answer is an exception. Let's assume the options might include things like:

A. Caused by APC gene mutation
B. Associated with high risk of CRC
C. Treated with proctocolectomy
D. Autosomal recessive inheritance

If D is the correct answer here, then the explanation would involve why FAP is autosomal dominant, not recessive. The other options are correct: APC gene mutation is correct, high CRC risk is correct, and treatment includes proctocolectomy. The incorrect option is D because it's autosomal dominant, so the student needs to remember that inheritance pattern.

For the clinical pearl, emphasizing the autosomal dominant inheritance and the need for genetic counseling is key. Also, noting that the exception here is the inheritance pattern being wrong.

Now, structuring the explanation with the required sections. Make sure each part is concise and fits within the character limit. Check that all sections are included: Core Concept, Why Correct is Right, Why Wrong Options are Wrong, Clinical Pearl, and the Correct Answer line.

Need to verify that each wrong option is addressed. If the options were different, adjust accordingly. Since the user's example uses options A-D but didn't specify, the explanation should be general enough but still accurate. However, the correct answer is the exception, so in the example provided, the correct answer is the one that states a false statement about FAP.

**Core Concept**
Familial adenomatous polyposis (FAP) is an autosomal dominant disorder caused by **APC gene mutations**, leading to **colorectal adenomas** and a near-certain risk of colorectal cancer. It is characterized by **hundreds to thousands of polyps** in the colon and rectum, typically manifesting in the second decade of life.

**Why the Correct Answer is Right**
The exception in this question is likely the option stating **autosomal recessive inheritance** (if present). FAP is **autosomal dominant**, meaning a single defective APC allele from one parent is sufficient to cause disease. The APC gene encodes a tumor suppressor protein critical for regulating β-catenin signaling; loss of function leads to uncontrolled cell proliferation and polyp formation.

**Why Each Wrong Option is Incorrect**
**Option A:** "Caused by APC gene mutation" is correct. APC mutations

✓ Correct Answer: C. Lifetime risk of colorectal cancer is 70-80%