[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?
ilikegreens
20-01-2009 11:29:07
Wow, 3 different answers, that must have helped him. Just to add to the pot... all of them are smart )
tylerc
20-01-2009 12:23:00
Great answer, considering it asks which ONE of the three men is smart?
JennyWren
20-01-2009 12:46:26
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.
[ufafbe9ef74]Aaron[/ufafbe9ef74]
!smart ->!Chem
smart -> Chem OR !Chem
[ufafbe9ef74]Brian[/ufafbe9ef74]
smart -> Chem
!smart -> Chem OR !Chem
[ufafbe9ef74]Colin[/ufafbe9ef74]
smart -> Phys
!smart -> !Phys
Next, let's label the possibilities for Aaron, Brian, and Colin being smart as [1], [2] and [3]. Remember that if Aaron is smart, Brian and Colin are not smart, etc.
[ufafbe9ef74]Aaron[/ufafbe9ef74]
[2] [3] !smart ->!Chem
[1] smart -> Chem OR !Chem
[ufafbe9ef74]Brian[/ufafbe9ef74]
[2] smart -> Chem
[1] [3] !smart -> Chem OR !Chem
[ufafbe9ef74]Colin[/ufafbe9ef74]
[3] smart -> Phys
[1] [2] !smart -> !Phys
Finally, we check each of these combinations, [1], [2], and [3], against the crucial condition, that "The smart man is the only man not to pass one of the two subjects".
If Colin is smart, [3] 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 [3] under Aaron, we see that this cannot be correct, because if this were the case, Aaron would also fail Chemistry.
If Brian is smart, [2] is in effect. [2] shows that Brian passes Chemistry, which means that the subject he does not pass must be Physics. However, [2] shows that Colin would ALSO fail Physics, so [2] cannot be correct.
If Aaron is smart, [1] is in effect. We know that Colin fails Physics when [1] 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 [1].
Thus, [1] is correct, and Aaron is the smart man.
manOFice
20-01-2009 13:13:51
[quotef90d19dea0="tylerc"]/head explodes[/quotef90d19dea0]
X2
EatChex89
20-01-2009 13:17:57
Jenny you are too smart.
I made it halfway thru and was even still confused. But congrats
bballp6699
20-01-2009 13:36:12
[quotecdfc5c4d88="JennyWren"]It's Aaron. Here's why.
[quotecdfc5c4d88="bballp6699"]Aaron[/quotecdfc5c4d88]
[/quotecdfc5c4d88]
Should be a good enough explanation.
akalic
20-01-2009 19:52:22
man this stuff reminds me of the stupid philosophy course i took (and aced )) logic and thinking
doylnea
20-01-2009 19:58:15
Nice work Jenny - that's exactly the kind of question that's on the LSAT if anyone is considering taking that test.
Powerbook
20-01-2009 20:09:42
[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? (