#13 - Most people who are skilled banjo players are also

[Administrator]

Complete Question Explanation

Must Be True. The correct answer choice is (D).

Answer choice (A):

Answer choice (B):

Answer choice (C):

Answer choice (D): This is the correct answer choice.

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[carnegie49]

I realize this conditional logic question can be solved by creating two hypothetical groups and a third overlapping group that fit the description of the stimulus. I just want to clarify---answer choice A could be but is NOT necessairly true, correct? It's possible but it does not have to be true and therefore is incorrect as the question demands a 'must be choice' to answer. Though we are not given hypothetical group sizes, conceivably in a given situation, A could be true (it could also, therefore, be false).

Answer choice D, conversely, must be true.

Is this thinking correct?

Thanks!

[Emily Haney-Caron]

Hi Carnegie,

Can you give an example of a situation in which you think A could be true? That will help me answer you better.

Basically, though, no - A cannot be true. For any numbers you come up with that follow the rules in the stimulus, there will be more people who are skilled at one or the other than are skilled at both. To see why, it might help to use an example. Let's say we have 100 people who are skilled at both banjo and guitar. We have at minimum 1 person who is skilled at just banjo. So, 101 people are skilled banjo players, and of those, 100 are also skilled guitar players. Now, since we have 100 people who are skilled at both, we have to have at least 101 people who are skilled at just guitar, giving us 201 people skilled at guitar and, of those, 100 skilled at both. We have 100 people skilled at both. The minimum number of people skilled at just guitar (101) plus the minimum number of people skilled at just banjo (1) will always be greater in total (102) than the minimum number of people skilled at both.

Does that make sense?

[carnegie49]

Yes, that really clarifies the matter. Thanks!!

[mpoulson]

Hello,

I am having real trouble following the explanation above even though it is well written. Can you explain in another way how to arrive at the answer? Thank you.

- Micah

[Clay Cooper]

Hi Micah,

Thanks for your question. Let me take a stab at it.

Imagine there are 100 skilled banjo players on earth. The stimulus tells us most skilled banjo players are skilled guitar players too, so that means we have at least 51 people who are skilled at both.

Now, the stimulus also tells us that most skilled guitar players are NOT also skilled banjo players. That means that the number of people who are skilled at both (at least 51, as we just proved) is not as big as the number of people who are skilled at only the guitar - so there must be at least 52 people who are skilled at guitar only.

So, how many people at a minimum are skilled at guitar if there are, as we specified in the beginning, 100 people skilled at banjo? At least the 51 that are skilled at both plus the 52 that are skilled at just guitar - so at least 103, which is greater than the 100 that are skilled just at banjo. So, no matter what, there are always more that are skilled at guitar than there are that are skilled at banjo, and D must be true.

Or, if you like math:

b = skilled at banjo
g = skilled at guitar
x = skilled at both

The stimulus tells us

x > .5b

and

g > 2x

We can multiply both sides of the first inequality by 2 to get:

2x > b

And now we have two inequalities concerning the term 2x, which we can link to say:

g > 2x > b

Therefore,

g > b.

Does that help?

[ClaudiaK32]

The post above was very helpful! Would you suggest that when we are in situations when mapping out the chain is not very useful, that we should choose numbers like you did?

[Charlie Melman]

Hi Claudia,

Yeah, I think that's a good idea. Questions like these, which refer to quantities of things, are best thought of in terms of numbers. That will allow you to put the abstract concepts in the question in concrete terms.

[tld5061]

HI,

Are there examples of other problems similar to this one you would recommend we practice to get comfortable with creating the examples w/ #s?

Thank you!

[Adam Tyson]

We have a whole chapter on Formal Logic in our Logical Reasoning Bible, tld5061! We don't cover it in the course material in our full length course, unfortunately, but that may not be too big a deal since it is not tested all that frequently compared to other types of reasoning. We mentioned the fading away of Formal Logic on the LSAT in this blog post:

http://blog.powerscore.com/lsat/is-the- ... g-stranger

You can study it on your own by just doing some searches online for that phrase - formal logic - and by finding the many discussions about it that we have had in this forum.

There is also some formal logic practice to be found in our materials about problems involving numbers and percentages (Lesson 9 in the full length course, if you happen to be taking that with us). Not all numbers and percentages problems involve formal logic, but many do, and formal logic always involves some math concepts like most, some, few, many, all, none, etc.

Finally, as you come across these questions on practice tests, ask yourself what you know about the numbers of the groups being talked about. Make numbers up if you have to. For example, if you are told that most people from New England are allergic to soy, pretend that there are 100 people from New England. In that case, at least 51, and perhaps all 100, are allergic to soy. Boom - you have something to work with!

Good luck with those, and if you come across any that give you trouble you can always come back here and ask for more help.