
Dear Dr. Math,
I have found the answer to this question but i need help on how to
explain it and part b. Can u give a hint or start at least to show me
how to do it?
Aurthur, Beth, Carlos, and Diane were discussing their geometry
grades. All of the statements were true.
Arthurs said If i get an A, then beth will get an A
Beth said If i get an A, Then Carlos will get an A
Carlos said If i get an A, then Diane will get an A
a. Only two of the students received an A. Which Two? Explain your
answer.
I think it would be Carlos and Diane that got the A. Correct? I need
a start or help on the explaining part.
b. How would the answer change to a. if Diane had said, If I get an
A, then Aurthur will get an A. Can you help me here?
 Sonia


Hi Sonia,
Tell me what makes you think that Carlos and Diane would be the two
that got the A. Did you do any checking? Was it just a guess? What
makes you think it was right? That'll give me a place to start to
help you.
 Doctor Jody, The Math Forum


Dear Dr. Math,
Okay i think that carlos and diane got an A because if any of the
others got the A such as Aurthur then Beth would have to get an A and
Carlos will have to too which would be more then two. So if Carlos
gets an A then Diane will get one too but no one else because Diane
didnt say anything about anyone else getting an A if she got one.
 Sonia


Hi Sonia,
That's exactly right! That's a good and complete explanation, and so
you have now completed part a. :^)
I have a feeling you can do part b, too. What do you think would
happen if Diane had said, "If I get an A, then Arthur will get an A"?
Could Carlos and Diane be the only two with an A, as you said for
part a?
Let me know if you need more help with it. Though, you didn't really
need me for part a. But I'm glad to help.
 Doctor Jody, The Math Forum


Dear Dr. Math,
Well.... I was think wouldnt that be a type of cycle. meaning that
all of them would get an A?
 Sonia


Hi Sonia,
Right, it would create a cycle. If one gets an A, then all of them
get an A, just as you said. So there couldn't be just two that get
an A.
You did a really good job solving the problems and explaining them.
Your reasoning has been very clear and complete. By complete, I mean
that you covered all the possibilities.
All I did was look at your reasoning and check it against the
problem. I didn't see any other possibilities, so I knew it was
right. Can you tell me where you thought the difficulties were? For
example, why you weren't sure about part a?
 Doctor Jody, The Math Forum


Dear Dr. Math,
the reason i asked was because the explaination and the answers
seemed so general and easy that I thought there was more to it then
that. Thank you very much for helping and enocouraging me to do the
problem. I hope you can be a great help on furthur math problems!
 Sonia


Hi Sonia,
Glad it worked for you! Hope to see you again.
 Doctor Jody, The Math Forum


