Set S = { a, b, c, d, e} What is the median of Set S?

Great question!

Target question: What is the median of Set S?

Since set S has an ODD number of values, the median of set S will equal the MIDDLEMOST value, when the 5 values are arranged in ascending order.
So, we need only determine how the 5 values would be arranged in ascending order.

Statement 1: The average of c and d is greater than the average of c and e
In other words, (c + e)/2 < (c + d)/2
Multiply both sides of the inequality by 2 to get: c + e < c + d
Subtract c from both sides to get: e < d
So, all statement 1 is telling us is that e < d
There are several possible scenarios that satisfy the condition that e < d. Here are two:
Case a: a < b < c < e < d, in which case the median is c
Case b: a < b < e < d < c, in which case the median is e
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The average of a and b is greater than the average of b and c
In other words, (b + c)/2 < (a + b)/2
Multiply both sides of the inequality by 2 to get: b + c < a + b
Subtract b from both sides to get: c < a
So, all statement 2 is telling us is that c < a
There are several possible scenarios that satisfy the condition that c < a. Here are two:
Case a: c < b < a < e < d, in which case the median is a
Case b: c < b < e < d < a, in which case the median is e
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that e < d
Statement 2 tells us that c < a
There are still several possible scenarios that satisfy both of these conditions. Here are two:
Case a: c < b < a < e < d, in which case the median is a
Case b: c < b < e < d < a, in which case the median is e
Since we cannot answer the target question with certainty, the COMBINED statements are NOT SUFFICIENT

Answer:

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