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Difficulty: EasyMust Be True / Most Strongly Supported

Every geological sample collected from the Eldoria Caldera that contains trace amounts of zircon crystals was formed during a pyroclastic eruption. Any sample formed during a pyroclastic eruption exhibits rapid silicate cooling. Furthermore, no sample that exhibits rapid silicate cooling contains large olivine grains.

Based on the information above, which of the following statements must be true?

  1. Any geological sample collected from the Eldoria Caldera that contains trace amounts of zircon crystals exhibits rapid silicate cooling.Answer
  2. B
    Any geological sample that exhibits rapid silicate cooling was formed during a pyroclastic eruption.
  3. No geological sample formed during a pyroclastic eruption contains large olivine grains.Answer
  4. D
    Every geological sample formed during an eruption that was not pyroclastic contains large olivine grains.
  5. E
    Any geological sample collected from the Eldoria Caldera that does not contain trace amounts of zircon crystals contains large olivine grains.

Answer

The statements establishing that any Eldoria Caldera sample with zircon crystals exhibits rapid silicate cooling, and that no sample formed during a pyroclastic eruption contains large olivine grains, must both be true.
Transitive conditional chaining guarantees that samples containing zircon crystals from the caldera undergo rapid silicate cooling, and that samples from pyroclastic eruptions do not contain large olivine grains.

Step-by-Step Solution

1
Diagram the formal conditional premises provided in the stimulus.
Zircon-bearing Eldoria sample implies Pyroclastic eruption; Pyroclastic eruption implies Rapid silicate cooling; Rapid silicate cooling implies No large olivine grains.
Formalizing the premises establishes the directional logic chains required for deduction.
2
Connect the transitive relationships across the conditional chain.
Zircon-bearing Eldoria samples must exhibit rapid silicate cooling, and pyroclastic samples cannot contain large olivine grains.
Valid deductions follow directly from following the arrows of implication from sufficient conditions to necessary conditions.
3
Evaluate the answer choices to identify which claims strictly follow without fallacy.
The two valid forward deductions must be true, whereas the other options commit conditional reversals or ungrounded negations.
In a Must Be True question, only choices that are 100% logically guaranteed by the premises are correct.

Key Concept

Conditional Chaining and Deductive Inferences
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Topics

Must Be True / Most Strongly Supported

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