There are three (a,b,c) variables and one equation (a^3b^4=c) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. There is, thus, high chance that C is the correct answer. Using the condition 1) and the condition 2), we get a=2. The answer is unique and the condition is sufficient. However, since this is one of key questions, integer question, we have to apply the common mistake type 4(A). From the condition 1), we get a^3b^4=5,000=2^35^4. The answer is a=2. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.