Difference between revisions of "2000 AMC 8 Problems/Problem 5"

(Created page with '==Problem== Each principal of Lincoln High School serves exactly one <math>3</math>-year term. What is the maximum number of principals this school could have during an <math>8<…')
 
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term, then in the next six years two more principals would serve, and the last year of the
 
term, then in the next six years two more principals would serve, and the last year of the
 
period would be the first year of the fourth principal's term. Therefore, the maximum
 
period would be the first year of the fourth principal's term. Therefore, the maximum
number of principals who can serve during an <math>8</math>-year period is <math>4</math>.
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number of principals who can serve during an <math>8</math>-year period is <math>4</math>, so the answer is <math>\boxed{C}</math>
 
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if the terms are divided <math>1/2 3 4/ 5 6 7/8</math>
<math>\boxed{1|2 3 4|5 6 7|8}</math>
 
  
 
==See Also==
 
==See Also==
 
 
{{AMC8 box|year=2000|num-b=4|num-a=6}}
 
{{AMC8 box|year=2000|num-b=4|num-a=6}}
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Latest revision as of 16:38, 15 January 2022

Problem

Each principal of Lincoln High School serves exactly one $3$-year term. What is the maximum number of principals this school could have during an $8$-year period?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 8$

Solution

If the first year of the $8$-year period was the final year of a principal's term, then in the next six years two more principals would serve, and the last year of the period would be the first year of the fourth principal's term. Therefore, the maximum number of principals who can serve during an $8$-year period is $4$, so the answer is $\boxed{C}$ if the terms are divided $1/2 3 4/ 5 6 7/8$

See Also

2000 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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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