#16 - Most successful entrepreneurs work at least 18 hours

[Bpark179]

I took prep test 49 and got hung up on one question in particular. Logical Reasoning Section 2 Question 16.
Basically it said:
"Most successful entrepreneurs work at least 18hrs a day. No one who works 18 hours has leisure time. All happy entrepreneurs have leisure time."
I understood why the correct answer was right, but I couldn't disprove (or prove in this case since the question asked which answer could be true EXCEPT...) answer choice C. Using the inference method in the powerscore LR bible, I was unable to prove why "some happy entrepreneurs are successful entrepreneurs".

SE--m-->18+
18---->~L
HE---->L

How can I prove: HE<--s--->SE ???
Like I said. I understand why it is correct, but I cannot prove it via the powerscore method using logic inferences. I've added my logic below from where I got stuck:

SE--m-->18+ -----> ~L ----> ~HE
This leads to SE--m--> ~HE (or SE <--s--> ~HE)
18+---->~HE = HE----> ~18+
HE---->L

The who thing seems circular and I never get close to a positive
HE<--s--->SE relationship. Can someone please tell me where my logic is flawed???

[Robert Carroll]

Bpark,

Your diagramming of the conditionals is correct. The issue is that the wrong answer choices are not things that can be proved, but things that could be true. They do not have to be true, so there is no need (or possibility) of proving them.

Since the first conditional says only that "most" successful entrepreneurs work at least 18 hours a day, it is possible (could be true!) that there is at least one successful entrepreneur that does not work at least 18 hours a day. In other words, "some successful entrepreneurs do not work at least 18 hours a day" is possible. It might not be true - we don't know. But the point is that we don't know for sure that its negation is true, so "some successful entrepreneurs do not work at least 18 hours a day" could be true.

The second conditional makes us sure that anyone who works at least 18 hours a day has no time for leisure activities. It's possible someone who works less than that does have time for leisure activities. That's good, because we know time for leisure activities is necessary in order to be happy. Thus, it's possible some successful entrepreneurs are happy.

Note: we don't know there are any such people. All we need to do is show that it's possible. Since we know only that "most" entrepreneurs have a certain quality, it's an open question (and thus meets the could be true standard) that the remainder lack that quality. And that remainder could be happy.

Robert Carroll

[suburbsinmymindseye]

Hi!

So my question is regarding when it is advisable to diagram LR questions.

I essentially never diagram them because I generally feel I have the logic clear enough in my head where I can deduce the correct answer without spending time writing anything down. I score on average -2 per LR section so I think this strategy is working decently well for me, but I would still like to improve.

This question in particular really spun my head when I first looked at it, which frustrated me because the conditional statements were so transparent, yet I couldn't keep track of all the relationships and deductions in my head. For high scorers, would this be an ideal question to diagram? Do you have any advice on how I can tell when I should diagram a question and when I should avoid spending time doing so?

Thanks!

[Paul Marsh]

Hi suburbsinmymindseye! Nice job on your continued success on the average LR section.

As someone who also rarely diagrams LR questions, this is one that I probably would diagram. The best LR questions to diagram are those with multiple conditional reasoning statements that can be strung together (like this problem). (It sounds like you probably have no trouble recognizing conditional reasoning, but just in case anyone needs a refresher, revisit Lesson 2 of the Course Book). When you're stringing together and manipulating conditionals and their contrapositives, it can be helpful to have all that written down. This holds especially true for Parallel and Parallel Flaw type stimuli that chain together conditionals, since you'll be referring back to those conditional chains for each answer choice.

Hope that helps!

[170Believer]

Hi!

I am having a hard time drawing out the conditional relationship for this question.

The first part states "Most successful entrepreneurs [SE] work at least 18hrs a day" which can be diagrammed SE -M->18hrs

The second statement states "No one who works at least 18hrs a day has time for leisure [L]" I initially took this to be interpreted as 18hrs <--|-->~L. However, based on the previous reply the correct diagram appears to be 18hr-->~L (without the double negative arrow). Can someone explain why the double negative arrow does not apply here? In the book an example of "No Xs are Ys" is diagrammed as X<--|-->Y, is this not the same as the statement in the stimulus "No one who works 18hrs has time for leisure" ?

However, even if I take 18hrs-->~L to be true, my diagram so far looks like this when combined:

SE--M-->18hrs-->~L

The last statement "All Happy Entrepreneurs have time for leisure" can be diagrammed as HE --> L. However, the contrapositive of this statement must be applied in order to combine it to the above diagram which now is:

SE--M-->18hrs-->~L-->~HE

Now to relate back to the answer choices:

Answer A: Can this answer be proven possible through the diagram? Or is it simply a possibility because we only know those who work 18hrs-->~L but we do not know that ~L-->18hrs, and since we cannot definitively prove that, it COULD be true and hence why this answer is incorrect?

Answer B: We can take our first part of the diagram SE--M-->18hrs, and changed it to SE<--S-->18hrs day. Hence proving this answer is true, and thus is not the correct answer.

Answer C: I struggled to show how this answer is possible. When reversing the above diagram I got:
HE --> L --> ~18hrs<--S-->~SE. Which comes down to be HE <--S--> ~SE which is not what this answer choice is claiming. Any idea on where I went wrong with this?

Answer D: I diagrammed this answer as 18hrs <--S--> HE. But using the diagram, when reversed, it goes HE --> L --> ~18hrs, which contradicts the answer and hence why this is the right answer.

Answer E: Again, based on the stimulus, we only know that MOST entrepreneurs work 18hrs a day, but this leaves open the possibility that some do not and hence why this answer COULD be true and is incorrect. --- Similar to Answer A, can this answer be diagrammed using the above diagram to show how this answer could be true?

I know I asked a couple questions in my post but I would appreciate any help for this question.

Thank you!

[Rachael Wilkenfeld]

Hi 170believer,

It looks like you are wanting to prove that certain answer choices can be true, rather than just looking for the one that cannot be true. In these questions, if you prove one answer choice cannot be true, that's it. You read all five, but your goal shouldn't be to prove the others could be true.

Your conditionals looked good!

For answer choice (A), this is possible because there's nothing connecting ~L to 18+. It's a mistaken reversal of a conditional from the stimulus, which is something that does not have to be true, but also does not have to be false.

Answer choice (B) Your reasoning is right on here---good work.

Answer choice (C) This one is possible because it's not ruled out by any of the conditional statements. Everything is possible by default. "Some happy entrepreneurs are successful" is consistent with "most successful entrepreneurs are unhappy. " It's not provably false, so it could be true.

Answer choice (D): Absolutely excellent logic here.

Answer choice (E): This one is not provably false, so again it's a could be true. We know about most entrepreneurs from the stimulus. However, that includes the possibility that it's only 51% so it's possible that some are not working 18+ hours a day. The conditionals don't contradict this one either, so it could be true.

Overall, it seems like you want more out of a could be true answer choice than it will always give you. Sometimes a could be true answer is provably true, like we see here in answer choice (B). But more often, it will just not be prevented by the stimulus. The nebulousness of could be true questions can feel shaky---I get it. But you need to get comfortable with that wide range of possible in a could be true answer choice. You need to recognize both when it's extremely likely to be true, as well as when it's fairly unlikely but still possible. That's why I always look for the cannot be true answer choice in these. I could think through each of the answer choices to think about how they could work for the stimulus. But usually, I'll go through much faster by saying "is this provably false?" No? Move on to the next answer choice.

Hope that helps!

[zoezoe6021]

I have a question about the logic diagram.

If I want to reverse "Successful Entrepreneurs ——most→ 18h → /leisure →/Happy “, what would the diagram be?

"Happy → Leisure ——a few → successful entrepreneurs " ?

[zoezoe6021]

I have a question about the logic diagram.

If I want to reverse "Successful Entrepreneurs ——most→ 18h → /leisure →/Happy “, what would the diagram be?

"Happy → Leisure ——a few → successful entrepreneurs " ?

Anybody can help?

In short, whether I can reverse A---most---→ B

[Rachael Wilkenfeld]

Hi Zoe,

The reversal for most is some. A most B reverses to B some A.

Most cats are domestic. Some domestic animals are cats. The "some" there could be anything from 1 to all.

For our example here, we know most successful entrepreneurs work 18 hour days. We can reverse that to say that some people who work 18 hr days are successful entrepreneurs. We can't be sure it's only a few---in fact, the only people who work 18 hour days could be successful entrepreneurs! That's consistent with the formal logic given above.

Hope that helps!