A certain list consists of 3 different numbers. Does the median of the

Since we know a list consists of three different numbers, then we can reward the target question as "Are the three numbers equally spaced?"
Don't forget that, when testing numbers for each statement, the values must satisfy the information in each statement.

1. Median = Mean if the set is symmterical around median. Symmetrical means lets say for a set a,b,c where b is median if a-b=c-b then Median = Mean
A-b = c-b
2b-c-a......(1)

Once we solve Statement A we get to the exact same equation so A is sufficient and quite direct

2. B is what seems indirect and requires 2 layers of thinking and has two methods to solve

a)Translation Method
What is mean?
Avg = Sum of 3 values in set/3
What is statement Telling us?
The sum of three values in set is = 3 times the value of one number in set

Avg = Sum of 3 values / 3
3*Avg = Sum of 3 values

Now interpret slowly Sum of 3 values which is our RHS (Right hand side of equation ) IS 3 times value of one number in set
Hence Avg = One number in set
Avg cannot be lowest or highest value and has to be middle number in an odd set (odd number of terms)

b)Logical Method
Lets say we couldn't translate properly. What do we now? The obvious doubt is Sum is 3 times of which number - smallest, middle or largest

Lets say three nos are a,b,c and a<b<c

Can sum be 3a??
Sum = a+b+c >3a Why??? Because we know that the three nos. are different and the two numbers are BIGGER than a so there is no way that the sum of 3 nos could be equal to three times the smallest number. [In which case would the sum be 3a? If all nos were same which violates our given info]

Can sum be 3c??
Sum = a+b+c <3c Why??? Because we know that the three nos. are different and the two numbers are SMALLER than c so there is no way that the sum of 3 nos could be equal to three times the largest number. [In which case would the sum be 3c? If all nos were same which violates our given info]

Hence only one option remains sum is equal to 3 times median. Once you transform this equation we get back to 2b = a+c which is exactly what we had to prove!