2009_10A_Worksheets.pdf - One can holds 12 ounces of soda...

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 (B) 8 (C) 9 (D) 10 (E) 11
2009 AMC 10 A, Problem #1 —
“Number of cans is an integer.”
Solution
Answer (E): Because
128
12
= 10
2
3
, there must be 11 cans.
Difficulty: Easy
NCTM Standard: Number and Operations Standard: judge the effects of such operations as
multiplication, division, and computing powers and roots on the magnitudes of quantities.
Mathworld.com Classification: Number Theory > Arithmetic > Multiplication and Division >
Division

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?
2009 AMC 10 A, Problem #2 —
2009 AMC 12 A, Problem #4 —
“The value of any combination of four coins that
includes pennies cannot be a multiple of 5 cents.”
Difficulty: Easy
NCTM Standard: Number and Operations Standard: compare and contrast the properties of
numbers and number systems, including the rational and real numbers, and understand complex
numbers as solutions to quadratic equations that do not have real solutions.
Mathworld.com Classification: Foundations of Mathematics > Mathematical Problems >
Unsolved Problems > Coin Problem

Which of the following is equal to 1 +
1
1 +
1
1+1
?
(A)
5
4
(B)
3
2
(C)
5
3
(D) 2 (E) 3
2009 AMC 10 A, Problem #3 —
2009 AMC 12 A, Problem #2 —
“NEED HINT.”
Solution
Answer (C): Simplifying the expression,
1 +
1
1 +
1
1+1
= 1 +
1
1 +
1
2
= 1 +
1
3
2
= 1 +
2
3
=
5
3
.
Difficulty: Medium-easy
NCTM Standard: Number and Operations Standard: understand meanings of operations and
how they relate to one another.
Mathworld.com Classification: Number Theory > Arithmetic > Fractions > Fraction

Eric plans to compete in a triathlon. He can average 2
miles per hour in the
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?