Final answer:
Using statement I alone, we can calculate the distance from A to C as 20 miles. Statement II alone does not provide enough information to make this calculation. Thus, the correct answer is option A.
Step-by-step explanation:
Lets us examine the information given in statements I and II to determine the distance from town A to town C.
Statement I Analysis
The distance from A to B is 25% more than the distance from C to B. We can represent the distance from C to B as 'x' miles. Therefore, A to B would be x + 0.25x = 1.25x miles. Since we are told that the distance from A to B is 100 miles, we can set up the equation 1.25x = 100. Solving for x gives us x = 80 miles, which is the distance from C to B. Consequently, the distance from A to C, which is the remainder of the trip from A to B, would be 100 - 80 = 20 miles.
Statement II Analysis
The distance from A to C is 1/4 the distance from C to B. If we denote the distance from A to C as 'y' miles, we can write the relationship as y = 1/4 times the distance from C to B. However, without the exact figures for either distance, this statement alone isn't sufficient to determine the distance from A to C.
Combining Statements I and II
When we combine the information from both statements, we get a clear picture of the situation. From statement I, we have figured out the distance from C to B and, subsequently, the distance from A to C. Statement II is consistent with the calculation from statement I, but does not offer any new information.
Therefore, the correct option is A: If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.