Competition · AMC preparation · step 4 of 4

AMC 8 2005: 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 2005 #1 grade 3+ arithmetic
Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the c…
AMC 8 2005 #2 grade 6+ arithmetic
Karl bought five folders from Pay-A-Lot at a cost of textdollar 2.50 each. Pay-A-Lot had a 20%-off sale the following da…
AMC 8 2005 #3 grade 5+ geometry-2d
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal B…
AMC 8 2005 #4 grade 5+ geometry-2d
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7…
AMC 8 2005 #5 grade 4+ arithmetic
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?
AMC 8 2005 #6 grade 5+ arithmetic
Suppose d is a digit. For how many values of d is 2.00d5 > 2.005?
AMC 8 2005 #7 grade 8+ geometry-2d
Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from…
AMC 8 2005 #8 grade 6+ arithmetic
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?
AMC 8 2005 #9 grade 8+ geometry-2d
In quadrilateral ABCD, sides AB and BC both have length 10, sides CD and DA both have length 17, and the measure of angl…
AMC 8 2005 #10 grade 4+ rate-ratio
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3…
AMC 8 2005 #11 grade 6+ rate-ratio
The sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounte…
AMC 8 2005 #12 grade 6+ arithmetic
Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. Ho…
AMC 8 2005 #13 grade 3+ geometry-2d
The area of polygon ABCDEF is 52 with AB=8, BC=9 and FA=5. What is DE+EF?
AMC 8 2005 #14 grade 5+ counting
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the…
AMC 8 2005 #15 grade 5+ geometry-2d
How many different isosceles triangles have integer side lengths and perimeter 23?
AMC 8 2005 #16 grade 4+ counting
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks…
AMC 8 2005 #17 grade 6+ rate-ratio
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?
AMC 8 2005 #18 grade 4+ number-theory
How many three-digit numbers are divisible by 13?
AMC 8 2005 #19 grade 8+ geometry-2d
What is the perimeter of trapezoid ABCD?
AMC 8 2005 #20 grade 5+ number-theory
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are…
AMC 8 2005 #21 grade 7+ counting
How many distinct triangles can be drawn using three of the dots below as vertices?
AMC 8 2005 #22 grade 7+ rate-ratio
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50%…
AMC 8 2005 #23 grade 8+ geometry-2d
Isosceles right triangle ABC encloses a semicircle of area 2π. The circle has its center O on hypotenuse AB and is tange…
AMC 8 2005 #24 grade 6+ arithmetic
A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displ…
AMC 8 2005 #25 grade 8+ geometry-2d
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle…

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