Competition · AMC preparation · step 4 of 4

AMC 10 2003A: all 25 problems

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

AMC 10 2003A #1 grade 3+ arithmetic
What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd countin…
AMC 10 2003A #2 grade 5+ arithmetic
Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than…
AMC 10 2003A #3 grade 6+ geometry-3d
A solid box is 15 cm by 10 cm by 8 cm. A new solid is formed by removing a cube 3 cm on a side from each corner of this…
AMC 10 2003A #4 grade 6+ rate-ratio
It takes Anna 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from scho…
AMC 10 2003A #5 grade 8+ algebra
Let d and e denote the solutions of 2x²+3x-5=0. What is the value of (d-1)(e-1)?
AMC 10 2003A #6 grade 6+ algebra
Define x ♡ y to be |x-y| for all real numbers x and y. Which of the following statements is not true? (A) x ♡ y = y ♡ x…
AMC 10 2003A #7 grade 7+ geometry-2d
How many non-congruent triangles with perimeter 7 have integer side lengths?
AMC 10 2003A #8 grade 7+ probability
What is the probability that a randomly drawn positive factor of 60 is less than 7?
AMC 10 2003A #9 grade 8+ algebra
Simplify ³√x³√x³√x√x.
AMC 10 2003A #10 grade 6+ geometry-3d
The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge-to-edge. One more cong…
AMC 10 2003A #11 grade 6+ arithmetic
The sum of the two 5-digit numbers AMC10 and AMC12 is 123422. What is A+M+C?
AMC 10 2003A #12 grade 7+ geometry-2d
A point (x,y) is randomly picked from inside the rectangle with vertices (0,0), (4,0), (4,1), and (0,1). What is the pro…
AMC 10 2003A #13 grade 7+ algebra
The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. W…
AMC 10 2003A #14 grade 4+ number-theory
Let n be the largest integer that is the product of exactly 3 distinct prime numbers d, e, and 10d+e, where d and e are…
AMC 10 2003A #15 grade 7+ probability
What is the probability that an integer in the set {1,2,3,...,100} is divisible by 2 and not divisible by 3?
AMC 10 2003A #16 grade 4+ number-theory
What is the units digit of 13²⁰⁰³?
AMC 10 2003A #17 grade 8+ geometry-2d
The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its c…
AMC 10 2003A #18 grade 8+ algebra
What is the sum of the reciprocals of the roots of the equation 2003/2004x+1+1/x=0?
AMC 10 2003A #19 grade 8+ geometry-2d
A semicircle of diameter 1 sits at the top of a semicircle of diameter 2, as shown. The shaded area inside the smaller s…
AMC 10 2003A #20 grade 7+ probability
A base-10 three digit number n is selected at random. Which of the following is closest to the probability that the base…
AMC 10 2003A #21 grade 7+ counting
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are a…
AMC 10 2003A #22 grade 8+ geometry-2d
In rectangle ABCD, we have AB=8, BC=9, H is on BC with BH=6, E is on AD with DE=4, line EC intersects line AH at G, and…
AMC 10 2003A #23 grade 6+ counting
A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For examp…
AMC 10 2003A #24 grade 4+ number-theory
Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the…
AMC 10 2003A #25 grade 6+ number-theory
Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100. Fo…

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