Competition · AMC preparation · step 4 of 4

AMC 8 2016: 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 2016 #1 grade 4+ arithmetic
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
AMC 8 2016 #2 grade 6+ geometry-2d
In rectangle ABCD, AB=6 and AD=8. Point M is the midpoint of AD. What is the area of △ AMC?
AMC 8 2016 #3 grade 6+ arithmetic
Four students take an exam. Three of their scores are 70, 80, and 90. If the average of their four scores is 70, then wh…
AMC 8 2016 #4 grade 6+ rate-ratio
When Cheenu was a boy, he could run 15 miles in 3 hours and 30 minutes. As an old man, he can now walk 10 miles in 4 hou…
AMC 8 2016 #5 grade 4+ number-theory
The number N is a two-digit number. • When N is divided by 9, the remainder is 1. • When N is divided by 10, the remaind…
AMC 8 2016 #6 grade 6+ arithmetic
The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these…
AMC 8 2016 #7 grade 8+ number-theory
Which of the following numbers is not a perfect square?
AMC 8 2016 #8 grade 5+ arithmetic, pattern
Find the value of the expression
AMC 8 2016 #9 grade 5+ number-theory
What is the sum of the distinct prime integer divisors of 2016?
AMC 8 2016 #10 grade 6+ algebra
Suppose that a * b means 3a-b. What is the value of x if 2 * (5 * x)=1
AMC 8 2016 #11 grade 6+ algebra, number-theory
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by…
AMC 8 2016 #12 grade 6+ rate-ratio
Jefferson Middle School has the same number of boys and girls. 3/4 of the girls and 2/3 of the boys went on a field trip…
AMC 8 2016 #13 grade 7+ probability, counting
Two different numbers are randomly selected from the set { - 2, -1, 0, 3, 4, 5} and multiplied together. What is the pro…
AMC 8 2016 #14 grade 5+ rate-ratio, arithmetic
Karl's car uses a gallon of gas every 35 miles, and his gas tank holds 14 gallons when it is full. One day, Karl started…
AMC 8 2016 #15 grade 6+ number-theory, algebra
What is the largest power of 2 that is a divisor of 13⁴ - 11⁴?
AMC 8 2016 #16 grade 7+ rate-ratio, algebra
Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, beca…
AMC 8 2016 #17 grade 4+ counting
An ATM password at Fred's Bank is composed of four digits from 0 to 9, with repeated digits allowable. If no password ma…
AMC 8 2016 #18 grade 4+ counting, arithmetic
In an All-Area track meet, 216 sprinters enter a 100-meter dash competition. The track has 6 lanes, so only 6 sprinters…
AMC 8 2016 #19 grade 6+ arithmetic, algebra
The sum of 25 consecutive even integers is 10,000. What is the largest of these 25 consecutive integers?
AMC 8 2016 #20 grade 6+ number-theory
The least common multiple of a and b is 12, and the least common multiple of b and c is 15. What is the least possible v…
AMC 8 2016 #21 grade 7+ probability, counting
A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all…
AMC 8 2016 #22 grade 8+ geometry-2d
Rectangle DEFA below is a 3 × 4 rectangle with DC=CB=BA=1. The area of the "bat wings" (shaded area) is
AMC 8 2016 #23 grade 7+ geometry-2d
Two congruent circles centered at points A and B each pass through the other circle's center. The line containing both A…
AMC 8 2016 #24 grade 4+ number-theory, logic
The digits 1, 2, 3, 4, and 5 are each used once to write a five-digit number PQRST. The three-digit number PQR is divisi…
AMC 8 2016 #25 grade 8+ geometry-2d
A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is…

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