Competition · AMC preparation · step 4 of 4

AMC 8 2014: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 8 2014 #1 grade 7+ arithmetic
Harry and Terry are each told to calculate 8-(2+5). Harry gets the correct answer. Terry ignores the parentheses and cal…
AMC 8 2014 #2 grade 3+ arithmetic
Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay…
AMC 8 2014 #3 grade 6+ arithmetic
Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three…
AMC 8 2014 #4 grade 4+ number-theory
The sum of two prime numbers is 85. What is the product of these two prime numbers?
AMC 8 2014 #5 grade 6+ rate-ratio
Margie's car can go 32 miles on a gallon of gas, and gas currently costs $4 per gallon. How many miles can Margie drive…
AMC 8 2014 #6 grade 4+ arithmetic
Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25, and 36. What is the sum of the areas…
AMC 8 2014 #7 grade 6+ rate-ratio
There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girls to the numb…
AMC 8 2014 #8 grade 5+ number-theory
Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solvin…
AMC 8 2014 #9 grade 8+ geometry-2d
In bigtriangleup ABC, D is a point on side AC such that BD=DC and ∠ BCD measures 70°. What is the degree measure of ∠ AD…
AMC 8 2014 #10 grade 4+ arithmetic
The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12 years old the year…
AMC 8 2014 #11 grade 7+ counting
Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks north of Jack's hou…
AMC 8 2014 #12 grade 7+ probability
A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures d…
AMC 8 2014 #13 grade 4+ number-theory
If n and m are integers and n²+m² is even, which of the following is impossible?
AMC 8 2014 #14 grade 8+ geometry-2d
Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE?
AMC 8 2014 #15 grade 8+ geometry-2d
The circumference of the circle with center O is divided into 12 equal arcs, marked the letters A through L as seen belo…
AMC 8 2014 #16 grade 7+ counting
The "Middle School Eight" basketball conference has 8 teams. Every season, each team plays every other conference team t…
AMC 8 2014 #17 grade 6+ rate-ratio
George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, an…
AMC 8 2014 #18 grade 7+ probability
Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of…
AMC 8 2014 #19 grade 6+ geometry-3d
A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are color…
AMC 8 2014 #20 grade 7+ geometry-2d
Rectangle ABCD has sides CD=3 and DA=5. A circle of radius 1 is centered at A, a circle of radius 2 is centered at B, an…
AMC 8 2014 #21 grade 6+ number-theory
The 7-digit numbers 7 4 A 5 2 B 1 and 3 2 6 A B 4 C are each multiples of 3. Which of the following could be the value o…
AMC 8 2014 #22 grade 3+ algebra
A 2-digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the u…
AMC 8 2014 #23 grade 6+ number-theory, logic
Three members of the Euclid Middle School girls' softball team had the following conversation. Ashley: I just realized t…
AMC 8 2014 #24 grade 6+ arithmetic, logic
One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. Wh…
AMC 8 2014 #25 grade 7+ geometry-2d, rate-ratio
A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composed of semicircles…

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