2025 AMC 8 Problem 2

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To help you master 2025 AMC 8 Problem 2, this page includes:

• The original AMC problem to try, plus the correct answer

• Clear, step-by-step solutions using different methods

• Key ideas, useful formulas, and takeaways you can apply to similar problems

• Related problems from past AMC exams, plus new practice problems that build the same skills

Want more practice? Scroll down to download Think Academy’s AMC 8 practice packs and keep building your AMC 8 skills.

2025 AMC8 Problem 2

Solution

Solution 1

Direct Translation and Addition Method

Determine the numerical value of each symbol using the provided table, multiply by how many times each symbol appears, and add them all together.

Step 1: Analyze the example to understand the system

The example states that $32$ is represented by three arches ($\cap$) and two vertical strokes ($|$). From the table, an arch is worth $10$ and a stroke is worth $1$. The total is calculated by adding their values. This confirms the system is additive.

$$3\times 10+2\times 1=30+2=32$$

Step 2: Identify and count the symbols in the given sequence

Looking at the second image from left to right, we identify the symbols using the table: – There is $1$ finger symbol. – There are $4$ spiral symbols. – There are $2$ arch symbols. – There are $3$ vertical stroke symbols. Notice that there is no flower symbol, which represents $1,000$.

Step 3: Calculate the total value

Multiply the count of each symbol by its corresponding value from the table, then add the results together.

$$1\times 10,000=10,000$$

$$4\times 100=400$$

$$2\times 10=20$$

$$3\times 1=3$$

$$10,000+400+20+3=10,423$$

Correct answer: B. $10,423$
The total is $10,423$, which matches choice B. We can verify this by checking that the digits in our answer match the counts of each symbol: a $1$ in the ten-thousands place, $0$ in the thousands, $4$ in the hundreds, $2$ in the tens, and $3$ in the ones.

Solution 2

Place Value Shortcut

Because the symbols represent powers of $10$, the Egyptian system maps directly to our place-value digits. A missing symbol means that specific place value has a digit of $0$.

Step 1: Find the missing place value

The highest-value symbol in the sequence is the finger, which represents $10,000$. The next symbol shown is the spiral, which represents $100$. The symbol for $1,000$ (the flower) is entirely missing from the sequence.

Step 2: Use the missing value to eliminate answer choices

Because the $1,000$ symbol is absent, the thousands digit in our base-10 number must be $0$. Let’s check the thousands digit of the given answer choices: – A. $1,423$ (thousands digit is $1$) – B. $10,423$ (thousands digit is $0$) – C. $14,023$ (thousands digit is $4$) – D. $14,203$ (thousands digit is $4$) – E. $14,230$ (thousands digit is $4$) Only choice B has a $0$ in the thousands place.

Correct answer: B. $10,423$
The correct answer is $10,423$ (Choice B). We can quickly verify the other digits ($1$ for $10,000$, $4$ for $100$, $2$ for $10$, $3$ for $1$) to ensure they perfectly match the visual counts.

Similar Problems in Real Exams

The following five AMC 8 problems are closely related to AMC 8 2025 Question 2. These real AMC 8 problems test the same key concept—Arithmetic Operations & Number Sense. Click any problem to learn and practice, then continue to the adapted practice section later in this article for more problems to try.

2026 AMC 8 Problem 1

2025 AMC 8 Problem 3

2023 AMC 8 Problem 1

2023 AMC 8 Problem 3

2020 AMC 8 Problem 3

Adapted Problems to Practice

What Formulas Do You Need for This Problem?

• Additive Numeral System:

Applies to systems like Egyptian hieroglyphs or Roman numerals (mostly). The example $32$ demonstrates that the Egyptian hieroglyphic system is additive, allowing us to simply count each symbol and sum their values.

• Base-10 Place Value:

Applies to modern Hindu-Arabic numerals. Because the Egyptian symbols correspond perfectly to powers of $10$, we can map the count of each symbol directly to the corresponding digits of a modern base-10 number.

Key Takeaway: Remember This Strategy for Next Time

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