Difference between revisions of "2008 AMC 10A Problems"
I like pie (talk | contribs) (Problem 9, typo in Problem 8) |
I like pie (talk | contribs) (Fixed Problem 1 LaTeX + Typo) |
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==Problem 1== | ==Problem 1== | ||
− | A bakery owner turns on | + | A bakery owner turns on his doughnut machine at <math>\text{8:30}\ {\small\text{AM}}</math>. At <math>\text{11:10}\ {\small\text{AM}}</math> the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? |
− | <math>\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}}</math> | + | <math>\mathrm{(A)}\ \text{1:50}\ {\small\text{PM}}\qquad\mathrm{(B)}\ \text{3:00}\ {\small\text{PM}}\qquad\mathrm{(C)}\ \text{3:30}\ {\small\text{PM}}\qquad\mathrm{(D)}\ \text{4:30}\ {\small\text{PM}}\qquad\mathrm{(E)}\ \text{5:50}\ {\small\text{PM}}</math> |
[[2008 AMC 10A Problems/Problem 1|Solution]] | [[2008 AMC 10A Problems/Problem 1|Solution]] |
Revision as of 23:58, 25 April 2008
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
A bakery owner turns on his doughnut machine at . At
the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
Problem 2
A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is . The ratio of the rectangle's length to its width is
. What percent of the rectangle's area is inside the square?
Problem 3
For the positive integer , let
denote the sum of all the positive divisors of
with the exception of
itself. For example,
and
. What is
?
Problem 4
Suppose that of
bananas are worth as much as
oranges. How many oranges are worth as much as
of
bananas?
Problem 5
Which of the following is equal to the product
Problem 6
A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of 3 kilometers per hour, bikes at a rate of 20 kilometers per hour, and runs at a rate of 10 kilometers per hour. Which of the following is closest to the triathlete's average speed, in kilometers per hour, for the entire race?
Problem 7
The fraction
simplifies to which of the following?
Problem 8
Heather compares the price of a new computer at two different stores. Store offers
off the sticker price followed by a
rebate, and store
offers
off the same sticker price with no rebate. Heather saves
by buying the computer at store
instead of store
. What is the sticker price of the computer, in dollars?
Problem 9
Suppose that
is an integer. Which of the following statements must be true about
?
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 has bases
and
and diagonals intersecting at
. Suppose that
,
, and the area of
is
. What is the area of trapezoid
?
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?
Problem 23
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Problem 24
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Problem 25
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