Directions: In the following question, three statements are given followed by two conclusions. You must assume the statements to be true even if they contradict commonly known facts. Decide which of the conclusions logically follow(s) from the statements.

Statements:
Some Quartz is not Obsidian
Only Basalt is Pumice
Some Basalt is Quartz

Conclusions:
I. No Quartz is Pumice
II. Some Pumice is not Obsidian

The correct answer is If neither conclusion I nor II follows.

Step 1: Understanding and converting the statements
Let us analyze each statement given in the question:
1. Some Quartz is not Obsidian: This is a particular negative statement. It tells us that there is at least some part of Quartz that does not overlap with Obsidian.
2. Only Basalt is Pumice: In traditional logical syllogism, the statement "Only A is B" converts to "All B is A". Thus, this statement translates to All Pumice is Basalt.
3. Some Basalt is Quartz: This is a particular affirmative statement indicating an intersection between the set of Basalt and the set of Quartz.

Step 2: Analyzing Conclusion I
Conclusion I: No Quartz is Pumice
We know that All Pumice is Basalt and Some Basalt is Quartz. The relationship between Quartz and Pumice is uncertain because Pumice is only specified as being inside Basalt, while Quartz overlaps with Basalt. Quartz may or may not overlap with Pumice in valid Venn diagram representations. Since a definite negative relationship cannot be established, Conclusion I does not logically follow.

Step 3: Analyzing Conclusion II
Conclusion II: Some Pumice is not Obsidian
We are given that Some Quartz is not Obsidian and All Pumice is Basalt. There is no direct relation provided between Pumice and Obsidian. It is entirely possible for all elements of Pumice to be contained within Obsidian without violating any of the given statements. Because this conclusion is not definitely true in all possible cases, Conclusion II does not logically follow.

Conclusion:
Since neither Conclusion I nor Conclusion II logically follows from the given statements, the correct choice is If neither conclusion I nor II follows.