LR Question 13 Explanation
QUESTION TEXT: Most people who are skilled banjo players are also…
QUESTION TYPE: Must be True
FACTS:
- 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.
More Resources for Must Be True Questions
- Conditional Reasoning Article: Learn about conditional statements on the LSAT.
- LR Diagrams Guide: Learn how to draw LR diagrams.
- Intro to Conditional Reasoning: This intro course lesson covers conditional reasoning basics.
- Intro Course lesson: This intro course lesson covers Must Be True questions.
- Mastery Seminar lesson: This LR Mastery seminar lesson covers must be true questions.
I think that the numbers example is much harder than a simple diagram for this kind of question relating groups/subsets of groups?
There’s 3 groups:
A – Skilled Banjo Players
B – Skilled Guitar Players
C – Skilled Banjo+Guitar Players
This question relates these 3 groups, which we can diagram with 3 squares, one to represent the # of people in each group.
1. Draw a square (A), representing Skilled Banjo Players.
2. Create a new square (C) within (A) by shading in more than half, but less than the whole square.
(Shading in much more than 1/2 is ideal, since “MOST (A) ARE (B)” is true up to 99.99+% and this makes it easier to see the answer.)
3. Create a new square (B) by extending (C) such that (C) makes up less than half of (B).
(Like before, making (C) much less than 1/2 is ideal, since “MOST (B) ARE NOT (C)” can be 0.01% and this makes it easier to see the answer.)
You will end up with a diagram where the area of A is much much smaller than the area of B, showing that # Skilled Banjo Players < # Skilled Guitar Players.
That’s a great way to visualize the relationships. If the stimulus and answer wasn’t clear to me, I would probably opt to understand it through something along the lines of a venn diagram, which aligns more with your approach.
That said, I think numbers offer the value of precision. Diagrams can help provide a general sense of proportion (which is indeed all you need here), but plugging in concrete values helps confirm that the relationships hold under different conditions. It may also make it easier to see why certain answer choices are incorrect, for example if “most” statements or the answer choice create specific numerical constraints.
Ultimately, it comes down to a matter of preference depending on how you personally process information, so do what feels intuitive to you.
I don’t see how we can make any judgments about quantity of either guitar players OR banjo players in this situation, since no quantities are mentioned in the stimulus. What if there were 100,000 banjo players in existence, at least 50,001 of whom also played guitar, but there were only 100 guitar players in existence, and 51 of them were not skilled banjo players?
Most banjo players are still guitar players, and most guitar players are not skilled banjo players, but in this case D is very clearly incorrect, 100 is not greater than 50,0001. I don’t see anything in the stimulus that requires the number of guitar and banjo players to be equal.
It’s because the most statements refer to each other. Look at your own quantities. You have stated that:
50,001 banjo players play guitar, and
there are only 100 guitar players
The two statements are contradictory. When thinking about quantities the statements have to be consistent with each other. The two groups don’t need to be equal, but because they are self referential the math works out so D is true.
You can pick any numbers you like – but only if they fit the two statements.
Note: This is an old comment but I wanted to clarify the point.