2020

2020 AMC8 Paper & Solutions Pick

12 selected sample solutions, number theory weight increased with prime factorization and divisibility. Geometry focuses on area.

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12 Sample Questions

40 Minutes

Max Score 25

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Exam Overview

>, Area.

DDifficulty

EasyQ1-10
MediumQ11-20
HardQ21-25

TTopics

Algebra30%

Geometry30%

Number Theory25%

Combinatorics15%

AAwards

Distinguished Honor Roll

Distinguished Honor Roll (Top 1%)

21+

Honor Roll

Honor Roll (Top 5%)

17+

Achievement Roll

Grade 6 and below · 15+ points

15+

Sample Problems

2020 AMC8 Sample Problems (12 questions)

Sample reference problems by difficulty — click an option to check your answer

Q1EasyArithmetic

Calculate the value of 48 ÷ 6 + 3 × 5.

A) 21

B) 25

C) 23

D) 27

E) 33

Steps

Multiply and divide first: 8 + 15 = 23

Answer: COrder of operations: multiplication and division before addition and subtraction

Q3EasyRatio

The ratio of boys to girls is 3:5, and the school has 240 students in total. How many fewer boys are there than girls?

A) 40

B) 80

C) 90

D) 120

E) 60

Steps

Each part = 240/8 = 30

90 boys and 150 girls, difference = 60

Answer: ERatio difference = (larger part - smaller part) × each part

Q5EasyArea

A circle has radius 7. Approximately what is its area? (π ≈ 3.14)

A) 43.96

B) 113.04

C) 196

D) 153.86

E) 307.72

Steps

Area = π × 7² = 3.14 × 49 ≈ 153.86

Answer: DArea of a circle = πr²

Q8EasyAverage

What is the mean of the data 12, 15, 18, 20, 25?

A) 16

B) 17

C) 19

D) 18

E) 20

Steps

Sum = 90

Mean = 90/5 = 18

Answer: DMean = sum ÷ number of values

Q11MediumKey concept: equations

The sum of two numbers is 50 and their difference is 12. What is the larger number?

A) 25

B) 28

C) 34

D) 31

E) 38

Steps

Let the larger number be a and the smaller be b

a + b = 50, a - b = 12

2a = 62 → a = 31

Answer: DSum-and-difference problem: larger number = (sum + difference)/2

Q13MediumPrime Factorization

How many positive divisors does 360 have?

A) 18

B) 20

C) 22

D) 28

E) 24

Steps

360 = 2³ × 3² × 5

Number of divisors = (3+1)(2+1)(1+1) = 4×3×2 = 24

Answer: EDivisor-count formula: add 1 to each prime factor's exponent, then multiply

Q14MediumArea

A rectangle's length is 3 times its width, and its perimeter is 48 cm. What is its area?

A) 96

B) 120

C) 108

D) 144

E) 192

Steps

2(w + 3w) = 48 → w = 6

Length = 18

Area = 108

Answer: CPerimeter of a rectangle = 2(length + width)

Q17MediumProbability

A number is chosen at random from 1 to 10. What is the probability that it is prime?

A) 2/5

B) 1/5

C) 3/10

D) 1/2

E) 3/5

Steps

Primes from 1 to 10: 2, 3, 5, 7 (4 of them)

Probability = 4/10 = 2/5

Answer: A1 is not prime, so be sure to exclude it

Q21HardNumber Theory

How many consecutive zeros are at the end of 100!?

A) 20

B) 22

C) 25

D) 24

E) 28

Steps

The number of trailing zeros = the power of 5 in 100!

⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24

Answer: DUse Legendre's formula to find the power of a prime factor in a factorial

Q22HardGeometry

A right triangle has legs 6 and 8. Find the altitude to the hypotenuse.

A) 3.6

B) 4

C) 5

D) 6

E) 4.8

Steps

Hypotenuse = √(36+64) = 10

Area = 1/2 × 6 × 8 = 24

Altitude to the hypotenuse = 2 × 24 / 10 = 4.8

Answer: ECompute the area of the same triangle two different ways

Q24HardLogic

Three people A, B, and C compete. It is known that A scored higher than B, and C scored lower than B. Which of the following must be true?

A) A 1st

B) A > C height

C) B 2nd

D) C 3rd

E) None necessarily true

Steps

A > B and B > C

So A > B > C, and A must be higher than C

A is 1st ✓, B is 2nd ✓, C is 3rd ✓

A higher than C must hold

Answer: BTransitivity: A > B and B > C → A > C

Q25HardCombinatorics

The numbers 1, 2, 3, 4, 5 are arranged in a row so that the odd positions hold odd numbers. How many such arrangements are there?

A) 6

B) 12

C) 18

D) 24

E) 36

Steps

Odd positions (1st, 3rd, 5th) hold the odd numbers (1, 3, 5): 3! = 6

Even positions (2nd, 4th) hold the even numbers (2, 4): 2! = 2

Total arrangements = 6 × 2 = 12

Answer: BUse the multiplication principle for step-by-step counting

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2020 AMC8 Paper & Solutions Pick

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2020 AMC8 Sample Problems (12 questions)

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