PrepTest 157, Section 3, Question 24
A smaller number of short documentary films than(36 more words not shown)
Which one of the following(13 more words not shown)
- AA greater number(28 more words not shown)
- BA greater number(38 more words not shown)
- CA smaller number(41 more words not shown)
- DA greater number(41 more words not shown)
- EA smaller number(39 more words not shown)
Reading the argument
The smaller group has more successes. Its success rate has to be higher.
Separate the three parts before looking for a parallel. First, fewer documentaries than science-fiction films succeed. Second, there are more documentaries overall. Those facts point in the same direction: documentaries have fewer successes spread across a larger group, while science fiction has more successes within a smaller group. So a higher percentage of science-fiction films succeed.
Try simple numbers. Suppose there are 100 documentaries with ten successes, and twenty science-fiction films with fifteen successes. That's ten percent versus seventy-five percent. The passage doesn't give those exact numbers, but they illustrate why the relationship works: more successful members and fewer total members produce the higher proportion.
What we’re looking for
This reasoning is valid. For the parallel, keep the count of successful members, the total size of each group, and the conclusion about percentages in their proper roles. The words “greater” and “smaller” can be rearranged without changing the meaning. What matters is which group has more of what, and which comparison is the conclusion.
Working the answers
- A
We get a comparison of the number of apartments with bathtubs and then a conclusion about percentages. But where is the comparison of the total numbers of apartments? That's the missing piece.
Imagine 100 small modern apartments, twenty with tubs, and twenty large Victorian apartments, ten with tubs. More modern apartments have tubs, but a smaller percentage of them do: twenty percent versus fifty percent. A's first fact can hold while its conclusion fails. The original avoids this problem by supplying the relative sizes of the groups.
- BCorrect
Match Victorian apartments to science-fiction films, modern apartments to documentaries, and having a freestanding bathtub to being commercially successful. There are more Victorian apartments with the target feature, even though there are fewer Victorian apartments overall. That's more successes within a smaller group.
The conclusion then compares proportions: a higher percentage of Victorian apartments have the feature. It uses both the count comparison and the group-size comparison to reach the percentage comparison, just like the film argument. All three pieces are present and doing the right jobs.
- C
This uses familiar ingredients but makes the count comparison the conclusion: fewer modern apartments have tubs. The word “For” introduces the support, including the percentage comparison. Our original does the opposite job with those statements: the count is evidence and the percentage is the conclusion. Repeating the same relationships doesn't preserve the reasoning if their roles change.
- D
Here the conclusion after “so” is that there are more modern apartments overall. The relative total sizes of the groups were a premise in the original, not what it was trying to establish. D uses the count and percentage comparisons to reach a group-size comparison. Again, the conclusion is the wrong piece.
- E
The count comparison starts correctly: fewer modern apartments have tubs. But now the answer says there are fewer modern apartments overall. The original's group with fewer successful members had more members overall. E reverses that crucial fact.
With a smaller group, fewer tubs could still mean a higher rate. Eight out of ten modern apartments would be eighty percent; ten out of 100 Victorian apartments would be only ten percent. E's counts and group sizes permit that result, so its claimed higher Victorian proportion doesn't follow.
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