SOLUTION: Albert has 3 daughters, Kate, Liz and Marina. 2 of them are Blonde and one, Brunette. If kate is Blonde, then so is Elizabeth; If Elizabeth is Blonde then so is Marina. Based on th
Algebra.Com
Question 332299: Albert has 3 daughters, Kate, Liz and Marina. 2 of them are Blonde and one, Brunette. If kate is Blonde, then so is Elizabeth; If Elizabeth is Blonde then so is Marina. Based on this information, which of the following is certainly true and why?
a) Liz is Brunette and Kate Blonde
b) Kate is Brunette and Marina Blonde
c) Marina and Elizabeth are Brunettes
d) Kate is Blonde, and Marina is Brunette
e) Kate and Liz are Blonde
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let A represent Kate is Blonde. Let B represent Liz is Blonde. Let C represent Marina is blonde.
If A then B.
Given
If B then C.Given
If A then C.Transitivity
But that means if A then B AND C which means that all three are blonde contradicting the given that 2 are blonde and 1 is not. Hence, Kate is not blonde which in turn implies that Liz and Marina are blonde.
Answer b. is the only one that fits.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
All of Lisa's friends except 2 have brown hair, all except 2 are blonde, and all except 2 (answered by ikleyn)
In a group of 40 children, 12 have blonde hair, 14 have brown eyes, and 5 have both... (answered by Boreal,richwmiller)
john and kate own stock .they each own half of the stock. if john gives kate 2/3 of his... (answered by mananth)
Kate is one year and six months younger than her sister. If her sister is 14 years and 2... (answered by josgarithmetic)
Pam and Kate are walking the same path. When Pam starts walking Kate is 60 feet ahead of... (answered by Boreal,josgarithmetic)
According to a recent survey, 50% of people have brown hair, 25% of people have blonde... (answered by math_tutor2020,ikleyn)
Kate has 2 more apples than she needs in order to have one-third of the apples that Renee (answered by stanbon,Aldorozos)
Donald,Kate and maggie win £2400 between them on the national lottery.Donald gets a share (answered by gonzo)
If 40% of a school are boys, and 30% of students have blond hair, and there are three... (answered by ankor@dixie-net.com)