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Difficulty: EasyDrawing Inferences and Valid Conclusions

During a three-year conservation project in Park Z, field researchers tracked native animal populations. The researchers found that whenever the population of wild rabbits decreased below 1,000 individuals, the population of red foxes consistently declined in the following year. Conversely, in years when the rabbit population was at or above 1,000, the red fox population never declined in the following year. Throughout both the second and third years of the project, the red fox population in Park Z experienced a decline. If the statements above are true, which of the following must also be true?

  1. The population of wild rabbits in Park Z was below 1,000 individuals in both the first and second years of the project.Answer
  2. B
    The red fox population in Park Z declined primarily due to a lack of alternative prey species.
  3. C
    In the third year of the project, the population of wild rabbits in Park Z reached zero.
  4. D
    The population of wild rabbits in Park Z remained at or above 1,000 individuals during the first year of the project.
  5. E
    Red foxes in Park Z rely exclusively on wild rabbits as their sole source of food.

Answer

The population of wild rabbits in Park Z was below 1,000 individuals in both the first and second years of the project.
The passage establishes that a red fox decline in a given year occurs if and only if the rabbit population was below 1,000 in the preceding year. Since the red fox population declined in both the second and third years of the project, the rabbit population must have been below 1,000 in both the first and second years.

Step-by-Step Solution

1
Analyze the conditional rules given in the passage.
Rabbit population < 1,000 in Year N leads to Red Fox decline in Year N+1. Rabbit population >= 1,000 in Year N prevents Red Fox decline in Year N+1.
This establishes a necessary and sufficient conditional link between the rabbit count in one year and the fox population trend in the following year.
2
Apply the observed outcomes for Years 2 and 3.
Red fox population declined in Year 2 (requiring Rabbit < 1,000 in Year 1) and declined in Year 3 (requiring Rabbit < 1,000 in Year 2).
By applying the contrapositive logic, any year experiencing a fox decline must have been preceded by a year with fewer than 1,000 rabbits.
3
Synthesize the valid logical deduction.
The rabbit population must have been below 1,000 during both Year 1 and Year 2.
This is the only conclusion that strictly must be true based solely on the provided premises.

Key Concept

Conditional Logic Deductions
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Topics

Drawing Inferences and Valid Conclusions

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