**Core Concept**
The question tests the understanding of glucose metabolism in starvation, focusing on the differing roles of **hexokinase** and **glucokinase** in the brain and liver. In starvation, the body's primary goal is to maintain blood glucose levels to ensure the brain's energy needs are met.

**Why the Correct Answer is Right**
The correct answer, **c) High km glucokinase**, is right because **glucokinase**, found in the liver, has a high Km (Michaelis constant) for glucose, meaning it has a low affinity for glucose. This allows the liver to only phosphorylate glucose when its levels are high, making it an important regulator of glucose metabolism. In contrast, the brain uses **hexokinase**, which has a low Km for glucose, allowing it to preferentially utilize glucose even at low concentrations.

**Why Each Wrong Option is Incorrect**
**Option A:** is incorrect because a low Km value of hexokinase is indeed a characteristic that allows the brain to utilize glucose preferentially, but this does not explain why the liver does not.
**Option B:** is incorrect because low Km glucokinase would imply the liver could utilize glucose at low concentrations, which is not the case.
**Option D:** is incorrect because high blood flow does not directly relate to the enzymatic preference for glucose in the liver.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that **glucokinase** acts as a glucose sensor in the liver, playing a critical role in the regulation of glucose metabolism, especially in the context of starvation or diabetes.

**Correct Answer:** C. High km glucokinase