PrepTest 151, Section 3, Question 24
A recent poll of a large number of(58 more words not shown)
The reasoning in the argument(6 more words not shown)
- Aignores the possibility(14 more words not shown)
- Btakes for granted(15 more words not shown)
- Cfails to consider(14 more words not shown)
- Dfails to consider(19 more words not shown)
- Eignores the possibility(10 more words not shown)
Reading the argument
Forty-seven percent of how many households?
A higher percentage in the cat group doesn't tell us that more degree holders live with cats. If the dog group is much larger, its smaller percentage could still represent many more people. The passage starts with pet-owning households and asks how many include a graduate. The conclusion starts with graduates and asks which pet they are more likely to live with. We can't simply swap those starting points.
Think of a rare pet, such as a tiger. Even if a very high percentage of tiger-owning households included a graduate, that wouldn't mean graduates were more likely to live with tigers than dogs. There might be very few tiger-owning households.
What we’re looking for
I might wonder whether income or where graduates live explains their pet choices. But first, do the numbers even establish the claimed pattern? For this flaw question, I'd focus on the missing group sizes.
Working the answers
- A
Some households could have both pets, but overlap isn't the central problem with comparing these percentages. The inference can fail even when the groups don't overlap at all, as the example in B shows. We need to consider the number of households behind each percentage, not just whether some belong to both categories.
- BCorrect
A much larger dog-owning population could produce more degree holders despite its lower percentage.
Imagine 100 cat-owning households and 1,000 dog-owning households, with no overlap. Forty-seven cat households and 380 dog households include a degree holder. To make this a clear example about individual people too, suppose each of those households has exactly one graduate. The reported percentages are true, yet 380 graduates live with dogs and only 47 live with cats. The conclusion goes the wrong way. Without accounting for the sizes of the groups, the author can't use the higher cat-group percentage to establish the claim about graduates.
- C
A household can include both a graduate and someone without a degree. Counting the nongraduates doesn't tell us how many graduates live in cat households versus dog households. It doesn't supply the missing sizes of the pet-owning groups.
- D
It doesn't matter whether the graduate chose the pet. The conclusion concerns the kind of household that person lives in. A graduate whose roommate selected the dog still lives in a dog-owning household. Decision-making power isn't needed to assess the claimed pattern.
- E
The author doesn't say a degree causes someone to live with a cat. The conclusion is about which household is more likely, so challenging a causal claim would challenge something the author never asserted. The mistake is moving between two different percentage comparisons without the numbers needed to do so.
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