Competition · AMC preparation · step 4 of 4

AMC 8 2008: 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 2008 #1 grade 3+ arithmetic
Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice as much on rides. How many dollars…
AMC 8 2008 #2 grade 4+ arithmetic
The ten-letter code BEST OF LUCK represents the ten digits 0-9, in order. What 4-digit number is represented by the code…
AMC 8 2008 #3 grade 4+ arithmetic
If February is a month that contains Friday the 13^th, what day of the week is February 1?
AMC 8 2008 #4 grade 3+ geometry-2d
In the figure, the outer equilateral triangle has area 16, the inner equilateral triangle has area 1, and the three trap…
AMC 8 2008 #5 grade 6+ rate-ratio
Barney Schwinn notices that the odometer on his bicycle reads 1441, a palindrome, because it reads the same forward and…
AMC 8 2008 #6 grade 6+ geometry-2d
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
AMC 8 2008 #7 grade 4+ arithmetic, rate-ratio
If 3/5=M/45=60/N, what is M+N?
AMC 8 2008 #8 grade 6+ arithmetic
Candy sales from the Boosters Club from January through April are shown. What were the average sales per month in dollar…
AMC 8 2008 #9 grade 7+ arithmetic
In 2005 Tycoon Tammy invested 100 dollars for two years. During the first year her investment suffered a 15% loss, but d…
AMC 8 2008 #10 grade 6+ arithmetic
The average age of the 6 people in Room A is 40. The average age of the 4 people in Room B is 25. If the two groups are…
AMC 8 2008 #11 grade 4+ counting
Each of the 39 students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twe…
AMC 8 2008 #12 grade 6+ arithmetic
A ball is dropped from a height of 3 meters. On its first bounce it rises to a height of 2 meters. It keeps falling and…
AMC 8 2008 #13 grade 6+ arithmetic
Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scal…
AMC 8 2008 #14 grade 7+ counting
Three A's, three B's, and three C's are placed in the nine spaces so that each row and column contain one of each letter…
AMC 8 2008 #15 grade 6+ arithmetic, number-theory
In Theresa's first 8 basketball games, she scored 7, 4, 3, 6, 8, 3, 1 and 5 points. In her ninth game, she scored fewer…
AMC 8 2008 #16 grade 6+ geometry-3d
A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface…
AMC 8 2008 #17 grade 4+ geometry-2d
Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All…
AMC 8 2008 #18 grade 7+ geometry-2d
Two circles that share the same center have radii 10 meters and 20 meters. An aardvark runs along the path shown, starti…
AMC 8 2008 #19 grade 8+ geometry-2d, counting
Eight points are spaced around at intervals of one unit around a 2 × 2 square, as shown. Two of the 8 points are chosen…
AMC 8 2008 #20 grade 6+ rate-ratio
The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and 3/4 of the girls passed the test,…
AMC 8 2008 #21 grade 8+ geometry-3d
Jerry cuts a wedge from a 6-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the v…
AMC 8 2008 #22 grade 6+ number-theory
For how many positive integer values of n are both n/3 and 3n three-digit whole numbers?
AMC 8 2008 #23 grade 6+ geometry-2d
In square ABCE, AF=2FE and CD=2DE. What is the ratio of the area of △ BFD to the area of square ABCE?
AMC 8 2008 #24 grade 8+ counting
Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled. What is the…
AMC 8 2008 #25 grade 7+ geometry-2d
Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius incr…

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