2003 AMC 8 Problem 17
Attempt Problem 17 of the 2003 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 8 solutions, or check the answer key.
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17.
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?
| Child | Eye Color | Hair Color |
|---|---|---|
| Benjamin | Blue | Black |
| Jim | Brown | Blond |
| Nadeen | Brown | Black |
| Austin | Blue | Blond |
| Tevyn | Blue | Black |
| Sue | Blue | Blond |
Nadeen and Austin
Benjamin and Sue
Benjamin and Austin
Nadeen and Tevyn
Austin and Sue
Answer: E
Small hint:
Jim’s siblings must each share eye color or hair color with Jim.
Big hint:
The two siblings must also share at least one characteristic with each other.
Solution:
Note that Nadeen, Austin, and Sue are the only individuals who share a characteristic with Jim. We need to find which of the are completely different from the others.
Austin and Sue both have blue eyes, which makes Nadeen the odd one out. Therefore, Austin and Sue are Jim’s siblings.
Thus, E is the correct answer.
Problem 17 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1993 AMC 8
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