Question

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

January $2$

January $12$

January $22$

February $11$

February $12$

Solution:

We can divide $10!$ by $60,$ $60,$ and $24$ to get the number of days that it takes for a unit of blood to expire.

The first division cancels a $6$ and $10.$ The second division cancels $3, 4,$ and $5.$ The final division cancels $8$ and turns the $9$ into a $3.$

This leaves $2, 7,$ and a $3,$ which multiply to $42.$ There are $31$ days in January, so by February $1,$ the blood only has $42 - 31 = 11$ days left.

$11$ days from February $1$ would make the blood expire on February $12.$

Thus, E is the correct answer.

2018 AMC 10A Problem 3

Solution:

Problem 3 in Other Years