[quote9a97cdc2b2]A Smart Man
Aaron, Brian and Colin are studying Chemistry and Physics.
Aaron says truthfully
1. Only one of us is smart.
2. If I am not smart, I will not pass Chemistry.
Brian says truthfully
3. The smart man is the only man not to pass one of the two subjects.
4. If I am smart, I will pass Chemistry.
Colin says truthfully
5. If I am smart, I will pass Physics.
6. If I am not smart, I will not pass Physics.
Which one of the three men is smart? [/quote9a97cdc2b2]
Friend needs this for a online class.. suggestions?
Wow, 3 different answers, that must have helped him. Just to add to the pot... all of them are smart )
Great answer, considering it asks which ONE of the three men is smart?
It's Aaron. Here's why.
Make a chart of the information we have. Note that being told something like "If I am not smart, I will not pass Chemistry" says nothing about whether or not you will pass if you ARE smart, so we must consider both as possible.
For ease of notation, !smart means not smart, Chem means passing Chemistry, !Chem means not passing Chemistry, same for Phys.
smart -> Chem OR !Chem
smart -> Chem
!smart -> Chem OR !Chem
smart -> Phys
!smart -> !Phys
Next, let's label the possibilities for Aaron, Brian, and Colin being smart as ,  and . Remember that if Aaron is smart, Brian and Colin are not smart, etc.
  !smart ->!Chem
 smart -> Chem OR !Chem
 smart -> Chem
  !smart -> Chem OR !Chem
 smart -> Phys
  !smart -> !Phys
Finally, we check each of these combinations, , , and , against the crucial condition, that "The smart man is the only man not to pass one of the two subjects".
If Colin is smart,  is in effect. Because he is smart, he passes Physics, which means that the subject he does not pass must be Chemistry, and he must be the ONLY man to fail Chemistry. But looking at the  under Aaron, we see that this cannot be correct, because if this were the case, Aaron would also fail Chemistry.
If Brian is smart,  is in effect.  shows that Brian passes Chemistry, which means that the subject he does not pass must be Physics. However,  shows that Colin would ALSO fail Physics, so  cannot be correct.
If Aaron is smart,  is in effect. We know that Colin fails Physics when  is in effect, so Aaron cannot be the only one to fail Physics, which means he must be the only one to fail Chemistry. Brian and Colin can both pass Chemistry under the conditions of .
Thus,  is correct, and Aaron is the smart man.
Jenny you are too smart.
I made it halfway thru and was even still confused. But congrats
[quotecdfc5c4d88="JennyWren"]It's Aaron. Here's why.
Should be a good enough explanation.
man this stuff reminds me of the stupid philosophy course i took (and aced )) logic and thinking
Nice work Jenny - that's exactly the kind of question that's on the LSAT if anyone is considering taking that test.
[quotefaf2ec34cc="doylnea"]Nice work Jenny - that's exactly the kind of question that's on the LSAT if anyone is considering taking that test.[/quotefaf2ec34cc]
Can I say screwed? (