2002 AMC 8 Problems/Problem 5

Problem

Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?

$\text{(A)}\ \text{Monday}\qquad\text{(B)}\ \text{Wednesday}\qquad\text{(C)}\ \text{Friday}\qquad\text{(D)}\ \text{Saturday}\qquad\text{(E)}\ \text{Sunday}$

Solution 1

Days of the week have a cycle that repeats every $7$ days. Thus, after $100$ cycles, or $700$ days, it will be Saturday again. Six more days will make it $\text{Friday} \rightarrow \boxed{C}$

Solution 2 (similar to solution 1)

Building off of solution 1, we can make things simpler by fast-forwarding $101$ cycles ( $707$ days) instead of $100$ cycles. Day $707$ would be a Saturday again, and one day before then (Day $706$ ) would be a Friday. Therefore the answer is $\boxed{(C)}$ .

2002 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AJHSME/AMC 8 Problems and Solutions

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2002 AMC 8 Problems/Problem 5

Contents

Problem

Solution 1

Solution 2 (similar to solution 1)

See Also