Step 1: Understanding the sentence structure.
The sentence compares Gauri's ability to play the keyboard with her sister's ability. Such a comparison requires a grammatically correct comparative phrase.
Step 2: Use of correct comparative expression.
The phrase as well as is used to show equality or similarity in ability or performance between two people. It correctly fits the context of the sentence.
Step 3: Eliminating incorrect options.
The expressions as better as, as nicest as, and as worse as are grammatically incorrect because comparative and superlative adjectives cannot be used in this structure.
Step 4: Conclusion.
Therefore, the correct and grammatically sound option is as well as.
Final Answer: (A) as well as