15. List S consists of 25 different integers. The least and greatest integers in S are 0 and 50, respectively. The integers in list T are obtained by adding 50 to each integer in S. List R consists of the 50 values in S and T combined. Quantity A: The median of the integers in R. Quantity B: 2 × the median of the integers in S.
Answer: C
The two quantities are equal.
The median of the integers in list R, which combines lists S and T, is equal to 2 times the median of the integers in list S. This is because the transformation applied to list S to create list T maintains the relative positions of the integers when combined.
A) Quantity A is greater.
This option is incorrect because the median of list R cannot be greater than 2 times the median of list S. Since list T is derived from list S by adding a constant to each element, the medians will align in a way that results in their equality when the two lists are combined.
B) Quantity B is greater.
This option is also incorrect. Similar to option A, the relationship between the medians of lists S and R, derived from the same set of numbers with a consistent transformation, ensures that Quantity B cannot exceed Quantity A.
C) The two quantities are equal.
This option is correct. The median of list R, which is the combined list of S and T, is effectively equal to 2 times the median of list S because all integers in T are just a shifted version of those in S, maintaining the balance needed for equality.
D) The relationship cannot be determined from the information given.
This option is incorrect. The relationship can be determined based on the known transformations from S to T. The consistent addition of 50 to each number in S directly influences the medians, allowing for a definitive conclusion.
Conclusion
The correct answer is that the two quantities are equal because the median of the combined lists S and T is precisely 2 times the median of list S. All other options fail to recognize the effect of the uniform transformation from S to T, which preserves the relationships between the medians. Thus, the equality holds true, confirming option C as the definitive answer.