21. List S contains 25 distinct integers from 0 to 50 inclusive. List T is formed by adding 50 to every integer in S. List R merges S and T. Quantity A: the median of R. Quantity B: twice the median of S.
Answer: C
The two quantities are equal.
The median of List R, which combines List S and List T, will equal twice the median of List S. This occurs because the integers in List T are simply the integers in List S each increased by 50, resulting in a symmetrical distribution around the median.
A) Quantity A is greater.
This option is incorrect because the median of List R does not exceed twice the median of List S. Since List T is a straightforward transformation of List S, the medians align in a way that keeps them equal.
B) Quantity B is greater.
This option is incorrect for the same reason as Option A. The transformation from List S to List T preserves the median relationship, making it impossible for twice the median of S to exceed the median of R.
C) The two quantities are equal.
This option is correct because the median of List R, which represents a set containing distinct integers paired with their transformed counterparts, results in a situation where the two quantities are equal due to the nature of the transformation applied.
D) The relationship cannot be determined from the information given.
This option is incorrect as the relationship can be definitively established based on how List T is derived from List S. The predictable nature of the transformation allows for a clear conclusion regarding the medians.
Conclusion
The correct answer is C, as the transformation from List S to List T results in a predictable and symmetrical relation that keeps the medians equal. All other options fail because they suggest a disparity that does not exist given the structure of the lists. Thus, the relationship between the two quantities is clear and determined.