Competition · AMC preparation · step 4 of 4

AMC 10 2003B: 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 2003B #1 grade 6+ arithmetic
Which of the following is the same as (2-4+6-8+10-12+14)/(3-6+9-12+15-18+21)?
AMC 10 2003B #2 grade 5+ arithmetic
Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs…
AMC 10 2003B #3 grade 7+ algebra
The sum of 5 consecutive even integers is 4 less than the sum of the first 8 consecutive odd counting numbers. What is t…
AMC 10 2003B #4 grade 5+ geometry-2d
Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, i…
AMC 10 2003B #5 grade 6+ rate-ratio
Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps e…
AMC 10 2003B #6 grade 8+ geometry-2d
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal l…
AMC 10 2003B #7 grade 8+ arithmetic
The symbolism ⌊ x ⌋ denotes the largest integer not exceeding x. For example, ⌊ 3 ⌋ = 3, and ⌊ 9/2 ⌋ = 4. Compute ⌊ √1 ⌋…
AMC 10 2003B #8 grade 8+ algebra
The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
AMC 10 2003B #9 grade 8+ algebra
Find the value of x that satisfies the equation 25⁻² = (5^(48/x))/(5^(26/x) · 25^(17/x)).
AMC 10 2003B #10 grade 6+ counting
Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed b…
AMC 10 2003B #11 grade 8+ algebra
A line with slope 3 intersects a line with slope 5 at point (10,15). What is the distance between the x-intercepts of th…
AMC 10 2003B #12 grade 7+ algebra
Al, Betty, and Clare split textdollar 1000 among them to be invested in different ways. Each begins with a different amo…
AMC 10 2003B #13 grade 2+ number-theory
Let ♣(x) denote the sum of the digits of the positive integer x. For example, ♣(8)=8 and ♣(123)=1+2+3=6. For how many tw…
AMC 10 2003B #14 grade 8+ number-theory
Given that 3⁸·5²=a^b, where both a and b are positive integers, find the smallest possible value for a+b.
AMC 10 2003B #15 grade 4+ number-theory
There are 100 players in a single tennis tournament. The tournament is single elimination, meaning that a player who los…
AMC 10 2003B #16 grade 6+ counting
A restaurant offers three desserts, and exactly twice as many appetizers as main courses. A dinner consists of an appeti…
AMC 10 2003B #17 grade 8+ geometry-3d
An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the…
AMC 10 2003B #18 grade 6+ number-theory
What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?
AMC 10 2003B #19 grade 8+ geometry-2d
Three semicircles of radius 1 are constructed on diameter AB of a semicircle of radius 2. The centers of the small semic…
AMC 10 2003B #20 grade 8+ geometry-2d
In rectangle ABCD, AB=5 and BC=3. Points F and G are on CD so that DF=1 and GC=2. Lines AF and BG intersect at E. Find t…
AMC 10 2003B #21 grade 7+ probability
A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red be…
AMC 10 2003B #22 grade 4+ arithmetic
A clock chimes once at 30 minutes past each hour and chimes on the hour according to the hour. For example, at 1 PM ther…
AMC 10 2003B #23 grade 8+ geometry-2d
A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF?
AMC 10 2003B #24 grade 8+ algebra
The first four terms in an arithmetic sequence are x+y, x-y, xy, and x/y, in that order. What is the fifth term?
AMC 10 2003B #25 grade 4+ number-theory
How many distinct four-digit numbers are divisible by 3 and have 23 as their last two digits?

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