PrepTest 145, Section 4, Question 13
Most people who are skilled banjo players are(17 more words not shown)
If the statements above are(10 more words not shown)
- AThere are more(27 more words not shown)
- BA person trying(27 more words not shown)
- CPlaying the guitar(8 more words not shown)
- DThere are more(19 more words not shown)
- EThere are more(19 more words not shown)
Reading the argument
The same people can be a majority of one group and a minority of another. Here, the people who play both instruments are a majority of the skilled banjo players but a minority of the skilled guitar players.
Use the numbers to make that concrete. Suppose there are 100 skilled banjo players and 51 of them are also skilled guitar players. That satisfies the first statement. Those same 51 people now count as the guitar players who also play banjo. To satisfy the second statement, more guitar players must be outside that shared group than inside it. We need at least 52 guitar-only players, giving us at least 103 guitar players in total.
What we’re looking for
For this must-be-true question, the particular numbers can change, but the relationship cannot. The shared group is more than half of all the banjo players and less than half of all the guitar players. The guitar group therefore has to be larger. Keep counting the same shared group from each side.
Working the answers
- A
This actually conflicts with the second statement. Most skilled guitar players are not skilled banjo players, so the guitar-only group already outnumbers the group who play both. Adding the banjo-only players to the people who play just one instrument only makes that one-instrument group larger. It cannot be smaller than the shared group.
- B
We know who is currently skilled at playing the instruments, not how many people tried to learn each one or what proportion succeeded. A larger group of skilled players could result from more people trying. It doesn't establish a better success rate for a learner.
- C
Nothing here compares how hard the instruments are to play. People might choose one instrument more often for many reasons. The overlap between skilled players doesn't establish which instrument takes more skill.
- DCorrect
The shared players are more than half of the banjo group but less than half of the guitar group, so the guitar group must be larger. Another way to see it: guitar-only players outnumber the shared players, and shared players outnumber banjo-only players. Therefore guitar-only players outnumber banjo-only players. Add the same shared players to each side, and the total guitar group is still larger.
- E
This puts the larger group on the wrong side. If the banjo group were larger than the guitar group, the shared players couldn't simultaneously be a majority of banjo players and a minority of guitar players. D gives the direction the two statements require.
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