Difference between revisions of "2003 AMC 8 Problems/Problem 17"
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==Solution== | ==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 <math>\boxed{\textbf{(E)}\ \text{Austin and Sue}}</math> are his siblings. | + | 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. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2003|num-b=16|num-a=18}} | {{AMC8 box|year=2003|num-b=16|num-a=18}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:47, 19 June 2019
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?
![\[\begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array}\]](http://latex.artofproblemsolving.com/0/a/e/0ae4f05da3c8e0d429452248f1039b98196d0c98.png)
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 
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.
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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