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Difficulty: MediumMust Be True / Most Strongly Supported

Archaeometallurgists analyzing ancient copper alloy artifacts recovered from an excavation site established the following facts:

• Every bronze artifact containing more than 2 percent arsenic was smelted using polymetallic sulfide ores.
• Any artifact smelted using polymetallic sulfide ores exhibits trace concentrations of nickel.
• No copper alloy artifact recovered from the lower stratigraphic layer of the site exhibits trace concentrations of nickel.

If the statements above are true, which one of the following must also be true?

  1. A
    Any artifact from the site that exhibits trace concentrations of nickel was smelted using polymetallic sulfide ores.
  2. B
    Every copper alloy artifact recovered from layers above the lower stratigraphic layer contains more than 2 percent arsenic.
  3. Any copper alloy artifact recovered from the lower stratigraphic layer contains no more than 2 percent arsenic.Answer
  4. D
    An artifact cannot exhibit trace concentrations of nickel unless it contains more than 2 percent arsenic.
  5. E
    Copper alloy artifacts recovered from the site were produced primarily for utilitarian rather than ceremonial purposes.

Answer

Any copper alloy artifact recovered from the lower stratigraphic layer contains no more than 2 percent arsenic.
The stimulus establishes that having over 2 percent arsenic guarantees polymetallic sulfide smelting, which in turn guarantees trace nickel (Arsenic > 2% → Polymetallic sulfide → Trace nickel). By contrapositive, any artifact lacking trace nickel cannot contain over 2 percent arsenic. Because no artifact from the lower stratigraphic layer contains trace nickel, every artifact from that layer must have 2 percent or less arsenic.

Step-by-Step Solution

1
Symbolize the formal conditional relationships established in the stimulus.
Let A = contains > 2% arsenic, S = smelted with polymetallic sulfide ores, N = exhibits trace nickel, and L = recovered from lower stratigraphic layer. Premise 1 gives A → S. Premise 2 gives S → N. Premise 3 gives L → not N.
Formalizing the premises allows clear evaluation of valid chain deductions and contrapositives.
2
Chain the conditional statements and determine their contrapositives.
Chaining premises 1 and 2 gives A → S → N (meaning A → N). The contrapositive is not N → not A (if an artifact does not exhibit trace nickel, it does not contain more than 2 percent arsenic).
The contrapositive of any valid conditional statement is logically equivalent to the original statement.
3
Synthesize the third premise with the derived contrapositive chain.
Since L → not N and not N → not A, it strictly follows that L → not A (any artifact from the lower layer does not contain > 2% arsenic, meaning it contains 2% or less).
Deductive chaining of valid conditionals guarantees the conclusion with absolute certainty.

Key Concept

Conditional Logic and Contrapositive Chaining
Estimated Time:1m 15s
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Topics

Must Be True / Most Strongly Supported

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