Its right, considering how you framed the statements. However, the framing is not as per the passage nor the question stem.

I believe your framing is based on the below (please correct if I am wrong):
You understood the passage correctly hence, Y > Q.
You took the conclusion as S > Y > Q (which is also fine)
Now you are looking at it from an inference question perspective i.e. based on the passage and the conclusion, which of the below options can be inferred.
Hence, came up with E i.e. S > Q can be inferred.


However, we are given the below:

Passage: X > P > Y > Q
Question stem states: in order for us to conclude S > Y with certainty, what additional information do I need ?
Options indicate these additional information.

How can you state that?

IMO, this question has two logical resolutions C and D, BUT only one correct answer, which is C

Premises:
P=>X
(Y=>P)^(Q=>Y)

Help with Y=>S ?

Solution: given all above premises and Y=>X, then

(A) Q and P melt at a higher temperature than S melts, S=>Q, S=>P <=> S=>S Not sufficient condition
(B) X melts at a higher temperature than S melts, S=>X Not sufficient condition
(C) P melts at a lower temperature than S melts, P=>S Sufficient to answer Yes, Y=>S
(D) Q melts at the same temperature that S melts, Q<=>S Sufficient to answer No, S=>Y BUT it is not required as addition by the question
(E) S melts at a higher temperature than Q melts, Q=>S Not sufficient condition

don't you think that its gonna b option E? we are confident that S>Q?

option C can be a possibility, means S can be and can not be greater than P ,
Now look at question statement that ''Y melts at a higher temperature than Q melts , and S melts at a higher temperature than Y melts'' it means S>Y>Q, in that way we are confident that S>Q (option E)

now I got it!
thank you sooo much for the productive explanation :0