SOLUTION: A mother rabbit has twelve baby bunnies. Six of the babies are brown, six of the babies have floppy ears, and six of the babies have long hair. All of the bunnies have at least one

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A mother rabbit has twelve baby bunnies. Six of the babies are brown, six of the babies have floppy ears, and six of the babies have long hair. All of the bunnies have at least one      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 242874: A mother rabbit has twelve baby bunnies. Six of the babies are brown, six of the babies have floppy ears, and six of the babies have long hair. All of the bunnies have at least one of these three traits. Two baby bunnies are brown and have floppy ears. Four baby bunnies are brown with long hair. Two baby bunnies have floppy ears and long hair but are not brown. One baby bunny is brown with long hair and floppy ears. Four baby bunnies are white with short hair and floppy ears. How many bunnies are brown with long hair, but don't have floppy ears? (Hint: If a baby bunny is brown with floppy ears, it may or may not have long hair--leave the option open until you are sure!)
I've tried making a bunch of Venn Diagrams, but I can't seem to come up with the right answer.
Thank you for your help.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Sorry, but either you, your teacher, or the book author
botched this problem.  Here is why:

The statement:

A:  six of the babies have floppy ears.

cannot be the case, because of these three statements:

B. Two baby bunnies have floppy ears and long hair but are not brown.  
C. One baby bunny is brown with long hair and floppy ears. 
D. Four baby bunnies are white with short hair and floppy ears. 

Neither of the two bunnies mentioned in statement B can be the bunny 
in statement C because that bunny is brown, and those two aren't brown. 
Also neither of the two bunnies in statement B can be among the four
bunnies mentioned in statement D because those have short hair, and the
two in statement B have long hair.
Furthermore the bunny mentioned in statement C cannot be any of the
four mentioned in statement D because those four have short hair and it
has long hair.

So statements B, C, and D account for seven different bunnies all with
floppy ears, yet statement A says there are 6.

Therefore the problem is inconsistent.  Unless, of course, the statement

"six of the babies have floppy ears"

can mean "six OR MORE", and I don't think they meant that. If you
can correct the problem, we can help you with it.

Edwin