10. 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 consists of 25 integers from List S and their corresponding 25 integers from List T (where each integer in S has been increased by 50), will be equal to twice the median of List S. This is due to the symmetrical nature of the integers in List T relative to their counterparts in List S.
A) Quantity A is greater.
This option suggests that the median of List R is greater than twice the median of List S. However, since List T is simply List S shifted upwards by 50, the distributions remain symmetrical, making this option incorrect.
B) Quantity B is greater.
This option posits that twice the median of List S exceeds the median of List R. Given that the median of R is derived from values that are symmetrically paired with those in S, this statement does not hold true.
C) The two quantities are equal.
This option correctly identifies that the median of List R will equal twice the median of List S. Each integer in S has a corresponding integer in T that maintains the necessary balance, confirming this equality.
D) The relationship cannot be determined from the information given.
This option implies a lack of clarity regarding the relationship between the two quantities. However, the structured formation of Lists S and T provides a clear basis for determining their medians, making this option incorrect.
Conclusion
The conclusion is that the medians of Lists R and S are related through a consistent mathematical transformation, leading to the finding that they are equal. As such, the choice indicating equality is the only correct answer, while all other options misinterpret the relationship established by the construction of the lists.