Set S has six numbers and their average (arithmetic mean) is 32. What

You didn't specify that the numbers are integers!!!
With current wording I would answer E.

the stem does not specify these numbers are integers and, in your calculation, you only use integer numbers!

Please check!

Can anyone help

I am concerned about the word SET S

The first Instant My understanding was SET doesn't contain repeated elements

Hence
(i) a,b,c,d,e,f (Numbers but not just Integers)]
a+b+c+d+e+f = 6*32 => sum(a,b,c,d,e,f) = 192

Case 1: 6*32 --> [32,32,32,32,32,32] -- Not possible since it is a Set (32 is repeating)
[31,32,32,32,32,33] -- Not Possible since it is a Set (32 is repeating)
[31,32,33,34,35,36] -- average not equals 32
Case2: since it is a set and all numbers are >=31
a can be 31,31.5,32,32.5 (considering a as lowest number)
if a = 31
(6/2)*[31+L] = 192
(3)*[31+L] = 192
[31+L] = 64
L = 33 ----> limitation this is considering series in AP (but condition of AP among numbers is missing)
hence first option is insufficient
(ii) set has 37
sum = 192
element in set = 37
rest sum = 192 - 37 => 155
[31,31,31,31,31,37]
[30,31,32,31,31,37]
[29,30,32,33,31, 37] -- median = 63/2
[28,29,33,34,31,37] -- median = 64/2
Not sufficient

Combining Both
[31,31,31,31,31,37] -- But S is set
Hence Answer is E

­You don't need to assume integers, even if you take the elements as numbers you'll get the same answer by combining the statements 31.

How on earth can a set have repeated (non-unique) numbers ? The answer should be E.