Examkin

Question

Difficulty: HardMost Strongly Supported Questions

In a comprehensive genetic study of an isolated Alpine ibex population, researchers discovered that any individual possessing the H4 allele also exhibited an unusually high metabolic rate. Furthermore, the researchers observed that a majority of the ibexes exhibiting this unusually high metabolic rate were resistant to a prevalent parasitic infection, *P. montanus*. However, not a single ibex possessing the H4 allele demonstrated resistance to *P. montanus*.

Which one of the following is most strongly supported by the researchers' findings?

  1. Less than half of the ibexes in the population that exhibit an unusually high metabolic rate possess the H4 allele.Answer
  2. B
    Any ibex in the population that exhibits an unusually high metabolic rate possesses the H4 allele.
  3. C
    Most of the ibexes in the population that do not possess the H4 allele are resistant to *P. montanus*.
  4. D
    The unusually high metabolic rate found in some ibexes is caused by the presence of the H4 allele.
  5. E
    A majority of the ibexes in the overall Alpine population are resistant to *P. montanus*.

Answer

Less than half of the ibexes in the population that exhibit an unusually high metabolic rate possess the H4 allele.
The stimulus establishes that every ibex with the H4 allele is part of the 'high metabolic rate' group, but absolutely none of them possess resistance to the parasite. However, we are also told that a *majority* (more than half) of the 'high metabolic rate' group *does* possess resistance. This means the non-resistant portion of the 'high metabolic rate' group must make up a minority (less than half). Since all of the H4 ibexes are forced into this non-resistant minority, the H4 ibexes themselves must constitute less than half of the 'high metabolic rate' group.

Step-by-Step Solution

1
Map the first conditional premise.
If an ibex has the H4 allele, it has a high metabolic rate (H4 -> High Metabolic Rate).
This establishes that the group of H4 ibexes is a subset of the group of ibexes with high metabolic rates.
2
Map the quantifier premise.
Most ibexes with a high metabolic rate are resistant to P. montanus (High Metabolic Rate -most-> Resistant).
This tells us that over 50% of the high metabolic rate group falls into the 'Resistant' category.
3
Map the final negative conditional premise.
If an ibex has the H4 allele, it is NOT resistant to P. montanus (H4 -> NOT Resistant).
This establishes the relationship between the H4 subset and the resistance characteristic.
4
Synthesize the mappings to find the numerical overlap.
Since all H4 ibexes have high metabolic rates but none are resistant, they must belong entirely to the portion of the high metabolic rate group that is NOT resistant.
Combining the subset rule (Step 1) with the negative constraint (Step 3) isolates where the H4 group fits within the larger metabolic group.
5
Determine the maximum size of the H4 group relative to the high metabolic rate group.
Because over 50% of the high metabolic rate group IS resistant, the non-resistant portion must be strictly less than 50%. Therefore, the H4 group (which is part of that non-resistant portion) must be less than half of the high metabolic rate group.
This mathematically proves the relationship required to select the correct answer.

Key Concept

Synthesizing conditional statements with formal logic quantifiers ('most', 'some', 'all') to deduce proportional limits.
Estimated Time:2m 0s
Rate this question

Topics

Most Strongly Supported Questions

More questions from this topic