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2008 AMC 10A Problems

Revision as of 20:42, 25 April 2008 by I like pie (talk | contribs) (→‎Problem 2)

Problem 1

A bakery owner turns on this doughnut machine at $8:30\ {\small\text{AM}}$. At $11:10\ {\small\text{AM}}$ the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?

$\mathrm{(A)}\ 1:50\ {\small\text{PM}}\qquad\mathrm{(B)}\ 3:00\ {\small\text{PM}}\qquad\mathrm{(C)}\ 3:30\ {\small\text{PM}}\qquad\mathrm{(D)}\ 4:30\ {\small\text{PM}}\qquad\mathrm{(E)}\ 5:50\ {\small\text{PM}}$

Solution

Problem 2

A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1$. The ratio of the rectangle's length to its width is $2:1$. What percent of the rectangle's area is inside the square?

$\mathrm{(A)}\ 12.5\qquad\mathrm{(B)}\ 25\qquad\mathrm{(C)}\ 50\qquad\mathrm{(D)}\ 75\qquad\mathrm{(E)}\ 87.5$

Solution

Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

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Problem 10

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Problem 11

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Problem 12

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Problem 13

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Problem 14

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Problem 15

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Problem 16

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Problem 17

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Problem 18

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Problem 19

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Problem 20

Trapezoid $ABCD$ has bases $\overline{AB}$ and $\overline{CD}$ and diagonals intersecting at $K$. Suppose that $AB = 9$, $DC = 12$, and the area of $\triangle AKD$ is $24$. What is the area of trapezoid $ABCD$?

$\mathrm{(A)}\ 92\qquad\mathrm{(B)}\ 94\qquad\mathrm{(C)}\ 96\qquad\mathrm{(D)}\ 98 \qquad\mathrm{(E)}\ 100$

Solution

Problem 21

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Problem 22

Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Jacob's sequence is an integer?

$\mathrm{(A)}\ \frac{1}{6}\qquad\mathrm{(B)}\ \frac{1}{3}\qquad\mathrm{(C)}\ \frac{1}{2}\qquad\mathrm{(D)}\ \frac{5}{8}\qquad\mathrm{(E)}\ \frac{3}{4}$

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Problem 23

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Problem 24

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Problem 25

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