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.

Rationale

The two quantities are equal.

When List S contains 25 distinct integers from 0 to 50, List T will contain those same integers increased by 50, ranging from 50 to 100. Merging both lists, List R will consist of integers from 0 to 100, with a total of 50 numbers, making the median of R equal to the average of the 25th and 26th numbers, which are 24 and 25. Since the median of S is also the average of its 25 numbers, the two medians end up being equal.

A (Quantity A is greater.) YOUR ANSWER

This choice suggests that the median of List R exceeds twice the median of List S. However, since both medians are equal, this relationship cannot hold true. Therefore, Quantity A being greater is incorrect.

B (Quantity B is greater.) YOUR ANSWER

This option posits that twice the median of List S is greater than the median of List R. Since both medians are equal, this statement cannot be true. Consequently, Quantity B being greater is also incorrect.

C (The two quantities are equal.) CORRECT

This is correct because the median of List R, which combines S and T, is calculated to be the same as twice the median of S. Since the 25 distinct integers in S are evenly distributed, the relationship holds true.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This choice implies that the relationship between the two quantities is indeterminate. However, since we can calculate the medians explicitly and demonstrate their equality, this statement is false.

Conclusion

Both medians of Lists R and S are equal, leading to the conclusion that the relationship between Quantity A and Quantity B is established clearly. Thus, the medians being equal confirms that neither quantity is greater, reinforcing that the two quantities are indeed equal.

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.

The two quantities are equal.

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