QUESTION TEXT: Most people who are skilled banjo players are…
QUESTION TYPE: Must be True
- Most skilled banjo players are skilled at guitar.
- Most skilled guitarists are not skilled at the banjo.
Drawing “most” statements will not help you on this question. This is a math question.
ANALYSIS: This preptest continues introducing new things. I’ve never seen knowledge of “most” statements tested in this way. (Possibly it has happened in very old preptests).
This is really a math problem. I’ll explain with an example. It’s always easy to use 100 with “most”: most of 100 is 51, at minimum. So, most banjo players are guitar players. That makes 100 banjo players, and 51 of them are also guitar players.
Now, the second statement: Most guitar players do not play the banjo. What can we do with this? We already know that 51 people play guitar and banjo. So we have to figure out what total number of guitar players works. Let’s consider three examples. In each example, I’ll assume that only 51 guitar players are skilled at the banjo. Each example has a different total number of guitar players:
- 51 guitar players. All 51 of them play the banjo. This very much contradicts the stimulus.
- 100 guitar players. 51 of them play the banjo, which is most. This contradicts the stimulus, which said less than most of guitar players play the banjo.
- 100+ guitar players. Only 51 of them play the banjo. So less than most guitar players play banjo and guitar. This is consistent with the stimulus.
So we need more guitar players than banjo players. And the middle case is at the limit. Above that, our statements are true.
Real numbers clear things up. Note that you can use any numbers. As long as the numbers are consistent with the stimulus, any set will work. I just choose 100 because it’s easy to work with when using most.
- This doesn’t have to be true. According to the math above, we could have 1,000,000 guitar players, almost none of whom play the banjo.
- We have no idea whether the guitar or the banjo is more difficult to play skillfully.
- Same as B. We know what portion of players are skilled players, but that tells us nothing about difficulty.
- CORRECT. See the analysis above. This is very hard to explain concisely. The gist is that the majority of guitar players do not play the banjo. Yet the majority of banjo players do play guitar, so there must be even more guitar players who don’t play the banjo to make up for it.
It’ll be clearer with real numbers.
- The opposite of the right answer. See the analysis above for numbers that explain why.
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