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Difference between revisions of "2003 AMC 8 Problems/Problem 17"

(Created page with "==Solution== <cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{B...")
 
 
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==Problem==
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The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?
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<cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array} </cmath>
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<math>\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}</math>
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<math>\textbf{(E)}\ \text{Austin and Sue} </math>
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==Solution==
 
==Solution==
  
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<cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array} </cmath>
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Jim has brown eyes and blonde hair. If you look for anybody who has brown eyes '''or''' blonde hair, you find that Nadeen, Austin, and Sue are Jim's possible siblings. However, the children have at least one common characteristics. Since Austin and Sue both have blonde hair, Nadeen is ruled out and therefore <math>\boxed{\textbf{(E)}\ \text{Austin and Sue}}</math> are his siblings. You can also see that in the hair color column, there are three black haired people and three blond haired people.  Since Jim has blond hair, all his siblings must be the other two with blond hair.
  
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Jim has brown eyes and blonde hair. If you look for anybody who has brown eyes '''or''' blonde hair, you find that Nadeen, Austin, and Sue are Jim's possible siblings. However, the children have at least one common characteristics. Since Austin and Sue both have blonde hair, Nadeen is ruled out and therefore <math> \textbf{(E)}</math> Austin and Sue.
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==Video Solution==
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https://youtu.be/W2xJGrFZyg0 Soo, DRMS, NM
  
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==See Also==
 
{{AMC8 box|year=2003|num-b=16|num-a=18}}
 
{{AMC8 box|year=2003|num-b=16|num-a=18}}
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{{MAA Notice}}

Latest revision as of 22:23, 22 March 2022

Problem

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?

\[\begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array}\]

$\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}$

$\textbf{(E)}\ \text{Austin and Sue}$

Solution

Jim has brown eyes and blonde hair. If you look for anybody who has brown eyes or blonde hair, you find that Nadeen, Austin, and Sue are Jim's possible siblings. However, the children have at least one common characteristics. Since Austin and Sue both have blonde hair, Nadeen is ruled out and therefore $\boxed{\textbf{(E)}\ \text{Austin and Sue}}$ are his siblings. You can also see that in the hair color column, there are three black haired people and three blond haired people. Since Jim has blond hair, all his siblings must be the other two with blond hair.

Video Solution

https://youtu.be/W2xJGrFZyg0 Soo, DRMS, NM

See Also

2003 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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