2022 AMC 8

Complete problem set with solutions and individual problem pages

Problem 7 Easy

When the World Wide Web first became popular in the 1990s, download speeds reached a maximum of about 56 kilobits per second. Approximately how many minutes would the download of a 4.2-megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)

  • A.

    0.6

  • B.

    10

  • C.

    1800

  • D.

    7200

  • E.

    36000

Answer:B

Solution 1

Notice that the number of kilobits in this song is 4.2 \cdot 8000 = 8 \cdot 7 \cdot 6 \cdot 100.

We must divide this by 56 in order to find out how many seconds this song would take to download: \frac{8 \times 7 \times 6 \times 100}{56} = \frac{56 \times 6 \times 100}{56} = 6 \times 100 = 600.

Finally, we divide this number by 60 because this is the number of seconds to get the answer \frac{600}{60}=\boxed{\textbf{(B) } 10}.

 

Solution 2

We seek a value of x that makes the following equation true, since every other quantity equals 1.

\frac{x\ \min }{4.2\ \text{mb}} \cdot \frac{56\ \text{kb}}{1\ \text{sec}} \cdot \frac{1\ \text{mb}}{8000\ \text{kb}} \cdot \frac{60\ \text{sec}}{1\ \min } = 1.

Solving yields x=\boxed{\textbf{(B) } 10}.

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