## Core Concept
The question tests understanding of protein separation techniques based on their properties. Proteins can be separated based on charge, size, or other specific properties. When two proteins have the same charge, methods that rely on charge differences (like ion exchange chromatography) are not effective.

## Why the Correct Answer is Right
Gel filtration chromatography, also known as size-exclusion chromatography, separates proteins based on their size (or molecular weight). This method is particularly useful when the proteins to be separated have similar charges, as it does not rely on charge differences. The technique works by passing the protein mixture through a column filled with porous beads. Smaller proteins can enter the pores and thus take a longer path through the column, eluting later than larger proteins which cannot enter the pores and pass through more quickly.

## Why Each Wrong Option is Incorrect
* **Option A:** Ion exchange chromatography separates proteins based on their charge. Since the two proteins in question have the same charge, this method would not be effective for their separation.
* **Option B:** Affinity chromatography is a technique that separates proteins based on a specific interaction between one protein and a ligand attached to a chromatographic matrix. While powerful, it is more specific to certain protein-ligand interactions and not generally used for separating proteins based on physical properties like size or charge.
* **Option C:** This option seems to be missing a technique but based on common chromatography methods, there might be confusion with hydroxyapatite chromatography or other specific types. However, without a clear technique listed, it's hard to directly refute.

## Clinical Pearl / High-Yield Fact
A key point to remember is that when dealing with proteins of similar charge, size-based separation techniques like **gel filtration chromatography** become particularly valuable. This technique does not require derivatization of the proteins and can be performed under relatively gentle conditions, preserving protein activity.

## Correct Answer: C. Gel filtration chromatography.