Q16 - Most successful entrepeneurs

[nanagyanewa]

Could someone please help me with this question, i eliminated down to A, C and D but I chose A because of the "anyone" because i thought that is too broad a scope. Could someone please help me understand why C is incorrect and why D is right? Thanks

[ManhattanPrepLSAT1]

Great question! I really love these ones testing conditional relationships.

The question asks us to find the one answer choice that cannot be true. The four incorrect answers will all be statements that could be true.

The easiest way to find a statement that cannot be true is to set up the three conditional relationships and then seek to either contradict one of them or an inference of two or more of the statements.

we know...

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

(Notation Key: SE = successful entrepreneurs, 18+ = works at least 18 hours a day, L = time for leisure, HE = happy entrepreneurs)

If we take the last two statements we can infer that
HE ---> ~18+

So it must be false that
HE some 18+

Answer choice (D) says that exactly and so must be false.

(A) could be true. We don't know what is true of people who do not have time for leisure.
(B) must be true from the first statement.
(C) could be true. The statements allow one to infer that most successful entrepreneurs are not happy, but that still leaves room for some to be happy.
(E) could be true. From the first statement we know that most successful entrepreneurs work at least 18 hours a day, but that still leaves room for some to work less than 18 hours a day.

Does that help you see this one a bit more clearly?

[nanagyanewa]

yea I guess I rushed through the question so I mis-read my diagram. I makes much sense now. Thanks!

[aust1n_chen]

I just had a quick question regarding conditionality statements with "some" i.e. given:
(SE some 18+)
what conclusions can I draw from that? Any special negation techniques?

[ManhattanPrepLSAT1]

I just had a quick question regarding conditionality statements with "some" i.e. given:
(SE some 18+)
what conclusions can I draw from that? Any special negation techniques?

What kinds of things do you have in mind? Something like the contrapositive for conditional statements?

Well unfortunately (or fortunately - depending on how you look at it), there are no contrapositives for "some" statements, and on contrapositives for "most" statements. Also, given that A some B, one cannot infer that A some ~B. Same goes for "most" statements.

The only cool thing you can do with "some" statements is run backwards across them. So if A some B, then you can infer that B some A.

And because we can always infer down from an "all" statement to a "some" statement, if we know that A ---> B, then we can infer that B some A.

Great question, thanks!

[moon]

Hello. I understand why (D) must be false, therefore, is our answer. But I have a problem understanding why (A) could be true.

If we know...

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

Isn't (A) presenting ~L ---> 18+, therefore illegal reversal of what was given? That's why I choose (A) in the first place.

Thank you!

[ohthatpatrick]

Hey, there.

Just be careful: you're confusing "Must Be False" with "Bad Inference". Those are actually different things.

Consider this statement:
All of Amanda's friends are 3rd graders.

Can we infer that "All 3rd graders are Amanda's friends"?

Absolutely not. Does the statement "all 3rd graders are Amanda's friends" contradict the statement that "all of Amanda's friends are 3rd graders"? No, it doesn't. They're compatible with each other. So an illegal reversal of a conditional still COULD be true, even though we have no reason for inferring it IS true.

A 'must be false' idea has to actively contradict what we know (not just stretch beyond what we can say).

If I tell you that "one of Amanda's friends is a 4th grader", then I have contradicted the idea that "all of Amanda's friends are 3rd graders". Those two ideas are incompatible (assuming we accept that you can't simultaneously be a 3rd AND a 4th grader).

(and even though we can't assume from A->B that B->A is also true, the reversal might be true. Consider this example, which works both ways:
- If the Oval Office at 1600 Pennsylvania Ave. is your office, then you're the President of the US)

Hope this helps.

[hnadgauda]

I interpreted A as a negation of "no one who works for at least 18 hours a day has time for leisure activities." Because of this, I marked A as my answer.

I know why D is is correct but I do not know why A is not correct. Can you explain what is wrong with my reasoning above?