2024 AMC 8 Real Questions and Analysis

In this article, you’ll find:

• A concise topic distribution (with a pie chart)
• The core concepts typically tested in each module
• A module-to-question mapping table for the 2024 AMC 8
• Five representative real questions with solutions and common mistakes
• Best resources to prepare for AMC 8

2024 AMC 8 Topic Distribution

The 2024 AMC 8 contains 25 multiple-choice questions completed in 40 minutes, emphasizing logical reasoning and conceptual understanding.

Learn more about AMC 8 Format and Scoring Here: AMC 8 FAQs: The Ultimate Guide for First-Time Test Takers

Detailed Module Analysis

Module	Question Numbers	What It Tests (Brief)
Geometry	3, 6, 11, 14, 24	area/length, triangle & coordinate geometry, shortest paths/geometry reasoning, composite figures
Word Problems	1, 2, 8, 9, 10, 12, 21	contextual arithmetic & rates, ratios/proportions, sequences in context
Number Theory	4, 15, 16, 19, 23	divisibility & remainders, digit/cryptarithm logic, prime/CRT style reasoning
Combinatorics	7, 13, 20, 25	tilings/arrangements, Catalan-style paths, ordering constraints, constructive counting
Probability & Statistics	5, 17, 18, 22	probability with dice/coins, averages/means, distribution/expected value

Real Questions and Solutions Explained

Geometry Example – Problem 11

Question:

The coordinates of △ABC are A(5,7), B(11,7), and C(3,𝑦) with 𝑦>7. The area of △ABC is 12. What is the value of 𝑦?

(A) 8 (B) 9 (C) 10 (D) 11 (E) 12

Solution:

Segment AB is horizontal with length 11−5=6, so use AB as the base.
\[ \frac12 \times 6 \times (𝑦-7) = 12 \]
\[ 3(𝑦-7)=12 \Rightarrow 𝑦-7=4 \Rightarrow 𝑦=11 \]

Answer: (D)

Common Mistakes:

• Using 𝑦 as the height directly without subtracting 7.
• Choosing a slanted side as the base and doing unnecessary distance calculations.
• Forgetting the \(\frac{1}{2}\) factor in the triangle area formula .

Word Problem Example – Problem 12

Question:

Rohan keeps a total of 90 guppies in 4 fish tanks.

• There is 1 more guppy in the 2nd tank than the 1st.

• There are 2 more in the 3rd than the 2nd.

• There are 3 more in the 4th than the 3rd.

How many guppies are in the 4th tank?

(A) 20 (B) 21 (C) 23 (D) 24 (E) 26

Solution:

Let the 1st tank have 𝑥. Then the four tanks have 𝑥, 𝑥+1, 𝑥+3, 𝑥+6.

\[4𝑥 + 10 = 90 \Rightarrow 𝑥 = 20\]

Fourth tank: \[𝑥 + 6 = 26\]

Answer: (E)

Common Mistakes:

• Treating the increases as consecutive from the first tank (e.g., 𝑥, 𝑥+1, 𝑥+2, 𝑥+3).
• Solving for 𝑥 correctly but reporting the first tank (𝑥) instead of the fourth (𝑥+6).

Number Theory Example – Problem 4

Question:

When Yunji added all the integers from 111 to 999 she mistakenly left out a number. Her incorrect sum turned out to be a perfect square. Which number did she leave out?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Solution:

The true sum is \[1 + 2 + \cdots + 9 = \frac{9 \times 10}{2} = 45\]

Perfect squares less than 45 are 36 and 25.

If the mistaken sum is 36, the omitted number is \[45 – 36 = 9\] which is valid. (If 25, the omitted number would be 20, which is not in the list.) Therefore, the omitted number is 9.

Answer: (E)

Common Mistakes:

• Forgetting the formula for \(1 + 2 + \cdots + n\).
• Checking 25 and stopping early, or subtracting in the wrong order (36 − 45).

Combinatorics Example – Problem 13

Question:

Buzz Bunny hops one step at a time up or down a set of stairs. In how many ways can Buzz start on the ground, make a sequence of 6 hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)

(A) 4 (B) 5 (C) 6 (D) 8 (E) 12

Solution:

To finish at ground after 6 hops, there must be 3 ups and 3 downs. Interpreting “stairs” as not going below ground, we count sequences that never dip below the start and return to ground — i.e., Dyck paths of semilength 3.

The five valid sequences are: UUUDDD, UUDUDD, UUDDUD, UDUDUD, UDUUDD.

The count equals the Catalan number: \[ C_{3} = \frac{1}{4} \times \frac{6!}{3!\,3!} = 5 \] Therefore, the number of ways is 5.

Answer: (B)

Common Mistakes:

• Counting all \( \frac{6!}{3!\,3!} = 20 \) up/down arrangements and ignoring the “no below ground” condition.
• Forgetting the path must start and end on ground.

Probability Example – Problem 5

Question:

Aaliyah rolls two standard 6-sided dice and notices the product is a multiple of 6. Which of the following integers cannot be the sum of the two numbers?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Solution:

“Product is multiple of 6” \(\Rightarrow\) at least one die is even and at least one die is a multiple of 3.

List all pairs satisfying both: (1,6), (2,3), (2,6), (3,6), (4,6), (5,6), (6,6).

Their sums are: 7, 5, 8, 9, 10, 11, 12. Among the given options, 6 never appears.

Answer: (B)

Common Mistakes :

• Requiring both dice to be multiples of 6.
• Missing pairs like (2,3).
• Counting all possible sums (5–12) and ignoring the product condition. 

2024 AMC 8 Answer Key

Question	Answer
1	B
2	C
3	E
4	E
5	B
6	D
7	E
8	D
9	E
10	B
11	D
12	E
13	B
14	A
15	C
16	D
17	E
18	A
19	C
20	D
21	E
22	B
23	C
24	B
25	C

Best Resources to Prepare for AMC 8

Visit All-in-one AMC8 Resource Hub: past papers, mock tests, and expert walkthroughs

Recommended Reading

• 2025 AMC 8 Real Questions and Analysis
• How to Prepare for AMC 8 Math Competition
• All About 2026 AMC 8: Dates, Registration, Scores and Prep Tips
• AMC 8 FAQs: The Ultimate Guide for First-Time Test Takers

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