2009 AMC 10A Problems

Problem 1

One can holds $12$ ounces of soda. What is the minimum number of cans needed to provide a gallon (128 ounces) of soda? $a)\, 7\qquad b)\, 8\qquad c)\, 9\qquad d)\, 10\qquad e)\, 11$

Solution

Problem 2

Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes and quarters. Which of the following could not be the total value of the four coins, in cents?

$a)\, 15\qquad b)\, 25\qquad c)\, 35\qquad d)\, 45\qquad e)\, 55$

Solution

Problem 3

Which of the following is equal to $1 + \frac{1}{1+\frac{1}{1+1}}$ ?

$a)\, \frac{5}{4}\qquad b)\, \frac{3}{2}\qquad c)\, \frac{5}{3}\qquad d)\, 2\qquad e)\, 3$

Solution

Problem 4

Eric plans to compete in a triathalon. He can average $2$ miles per hour in the $\frac{1}{4}$ -mile swim and $6$ miles per hour in the $3$ -mile run. His goal is to finish the triathlon in $2$ hours. To accomplish his goal what must his average speed in miles per hour, be for the $15$ -mile bicycle ride?

$a)\, \frac{120}{11}\qquad b)\, 11\qquad c)\, \frac{56}{5}\qquad d)\, \frac{45}{4}\qquad e)\, 12$

Solution

Problem 5

What is the sum of the digits of the square of $111,111,111$ ?

$a)\, 18\qquad b)\, 27\qquad c)\, 45\qquad d)\, 63\qquad e)\, 81$

Solution

Problem 6

Solution

Problem 7

A carton contains milk that is $2$ % fat, an amount that is $40$ % less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?