2018 AMC 10A Problems/Problem 3

Problem

A unit of blood expires after $10!=10\cdot 9 \cdot 8 \cdots 1$ seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire?

$\textbf{(A) }\text{January 2}\qquad\textbf{(B) }\text{January 12}\qquad\textbf{(C) }\text{January 22}\qquad\textbf{(D) }\text{February 11}\qquad\textbf{(E) }\text{February 12}$

Solution 1

There are $10!$ seconds that the blood has before expiring and there are $60 \cdot 60 \cdot 24$ seconds in a day. Dividing $\frac{10!}{60 \cdot 60 \cdot 24}$ gives $42$ days. $42$ days after January 1 is $\fbox{\textbf{(E) }\text{February 12}}$ .

Solution 2

$10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ . Convert $10!$ seconds to minutes: $9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2$ minutes. Convert minutes to hours: $9\cdot 8\cdot 7\cdot 2$ hours. Convert hours to days: $3\cdot 7\cdot 2 = 42$ days.

$42$ days after January 1 is $\fbox{\textbf{(E) }\text{February 12}}$

  ~Nosysnow | wonsysoN~

2018 AMC 10A (Problems • Answer Key • Resources)
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2018 AMC 10A Problems/Problem 3

Contents

Problem

Solution 1

Solution 2

See Also