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.
The two quantities are equal.
Since List S contains 25 different integers ranging from 0 to 50, the median of S is the average of the 12th and 13th integers when arranged in order. In List T, each integer in S is increased by 50, resulting in integers ranging from 50 to 100. When combined into List R, the median will still be the average of the 12th and 13th integers, which will also be 50 plus the average of the 12th and 13th integers of S. Therefore, the median of R is equal to 50 plus the median of S, which mathematically equates to 2 times the median of S.
This choice suggests that the median of integers in List R exceeds twice the median of List S. However, since the median of R is calculated to be equal to twice the median of S, this choice is incorrect.
This choice implies that twice the median of List S is greater than the median of List R. However, as derived earlier, the median of R equals twice the median of S, making this choice also incorrect.
This choice is accurate because the median of List R, which includes both S and T, is mathematically shown to be equal to twice the median of List S. This relationship holds true due to the properties of the median and the transformation applied to the integers in List T.
This choice suggests that there is insufficient information to compare the two quantities. However, we can definitively establish the relationship based on the medians of the lists, making this choice incorrect.
The analysis of the medians in Lists R and S reveals that they are equal when considering the transformation applied to List S to create List T. Thus, both quantities, Quantity A and Quantity B, are equal, affirming that the relationship between them can be precisely determined based on the given data.
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