Difference between revisions of "2011 AMC 12A Problems"
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== Problem 9 == | == Problem 9 == | ||
+ | At a twins and triplest convention, there were <math>9</math> sets of twins and <math>6</math> sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place? | ||
+ | |||
+ | <math> | ||
+ | \textbf{(A)}\ 324 \qquad | ||
+ | \textbf{(B)}\ 441 \qquad | ||
+ | \textbf{(C)}\ 630 \qquad | ||
+ | \textbf{(D)}\ 648 \qquad | ||
+ | \textbf{(E)}\ 882 </math> | ||
+ | |||
[[2011 AMC 12A Problems/Problem 9|Solution]] | [[2011 AMC 12A Problems/Problem 9|Solution]] | ||
== Problem 10 == | == Problem 10 == | ||
+ | A pair of standard <math>6</math>-sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference? | ||
+ | |||
+ | <math> | ||
+ | \textbf{(A)}\ \frac{1}{36} \qquad | ||
+ | \textbf{(B)}\ \frac{1}{12} \qquad | ||
+ | \textbf{(C)}\ \frac{1}{6} \qquad | ||
+ | \textbf{(D)}\ \frac{1}{4} \qquad | ||
+ | \textbf{(E)}\ \frac{5}{18} </math> | ||
+ | |||
[[2011 AMC 12A Problems/Problem 10|Solution]] | [[2011 AMC 12A Problems/Problem 10|Solution]] | ||
Revision as of 21:22, 9 February 2011
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 cell phone plan costs dollars each month, plus
cents per text message sent, plus
cents for each minute used over
hours. In January Michelle sent
text messages and talked for
hours. How much did she have to pay?
Problem 2
There are coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
Problem 3
A small bottle of shampoo can hold milliliters of shampoo, whereas a large bottle can hold
milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
Problem 4
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of ,
, and
minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?
Problem 5
Last summer $30%$ (Error compiling LaTeX. Unknown error_msg) of the birds living on Town Lake were geese, $25%$ (Error compiling LaTeX. Unknown error_msg) were swans, $10%$ (Error compiling LaTeX. Unknown error_msg) were herons, and $35%$ (Error compiling LaTeX. Unknown error_msg) were ducks. What percent of the birds that were not swans were geese?
Problem 6
Solution
The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was points. How many free throws did they make?
Problem 7
A majority of the students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than
. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was
. What was the cost of a pencil in cents?
Problem 8
In the eight term sequence ,
,
,
,
,
,
,
, the value of
is
and the sum of any three consecutive terms is
. What is
?
Problem 9
At a twins and triplest convention, there were sets of twins and
sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?
Problem 10
A pair of standard -sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference?