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Question

Difficulty: MediumNecessary Assumption

Materials Scientist: A new synthetic polymer, Elastium, is being adopted for manufacturing outdoor climbing ropes. Laboratory tests demonstrate that individual Elastium fibers are 30 percent more resistant to physical abrasion than the nylon fibers currently used in standard climbing ropes. Therefore, climbing ropes constructed entirely from Elastium will have a significantly longer safe-usage lifespan than current nylon climbing ropes.

Which of the following are assumptions on which the materials scientist's argument depends? (Select all that apply)

  1. The increased abrasion resistance of individual Elastium fibers results in a corresponding increase in the abrasion resistance of ropes woven from those fibers.Answer
  2. Elastium ropes do not degrade from other environmental factors, such as ultraviolet exposure, much more rapidly than nylon ropes do.Answer
  3. C
    Physical abrasion is the only factor that dictates the safe-usage lifespan of a climbing rope.
  4. D
    The manufacturing process for Elastium climbing ropes is no more expensive than the process for nylon ropes.
  5. E
    Current nylon climbing ropes frequently fail to meet the minimum safety standards required for outdoor climbing.

Answer

The correct options are the one stating that individual fiber resistance transfers to the woven rope, and the one stating Elastium does not degrade much more rapidly from other environmental factors.
The argument relies on two distinct assumptions. First, it assumes a part-to-whole relationship: that the superior abrasion resistance of individual Elastium fibers actually translates into superior abrasion resistance for the entire woven rope. If it does not, the conclusion fails. Second, it assumes that Elastium does not suffer from a separate, unstated vulnerability (such as rapid UV degradation) that would offset its superior abrasion resistance and shorten its overall safe-usage lifespan. Both of these unstated premises must be true for the conclusion to remain logically viable.

Step-by-Step Solution

1
Identify the core argument components.
Premise: Elastium fibers are 30% more resistant to physical abrasion than nylon fibers. Conclusion: Elastium ropes will have a significantly longer safe-usage lifespan.
Isolating the premise and conclusion highlights the logical gaps that must be bridged or defended.
2
Identify gaps in the reasoning (Bridge gaps).
The argument jumps from the properties of 'individual fibers' to the properties of the 'completed rope'. It assumes the strength of the parts translates to the strength of the whole.
Necessary assumptions often bridge new terms or scope shifts between the premise and conclusion.
3
Identify potential vulnerabilities (Defender gaps).
The argument assumes that abrasion is the determining factor for lifespan and that Elastium doesn't have some other fatal flaw (like UV degradation) that would shorten its lifespan compared to nylon.
Arguments projecting a positive outcome must assume there are no unstated overriding negatives.
4
Apply the Negation Test to candidate answers.
Negating the part-to-whole transfer ruins the conclusion. Negating the defense against other degradation factors (meaning Elastium DOES degrade much faster from other things) ruins the conclusion.
A valid necessary assumption must invalidate the argument when it is rendered logically false.

Key Concept

Necessary Assumption
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Topics

Necessary Assumption

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