AMC 8 · 2002 · #8

Grade 2 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Weighted Group Aggregation

graph-readingmulti-digit-arithmetic identify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 1 insight 📊 Diagram

Problem

Problems 8,9 and 10 use the data found in the accompanying paragraph and table:

Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and
France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)

How many of his European stamps were issued in the '80s?

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 8 2002 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

Try it yourself first — the explanation is most useful after you’ve attempted it.

View mode:

Toolkit + CCSS Solution

Understand

Restated: Juan's stamp collection is organized in a table by country (rows) and decade of issue (columns). Brazil, France, Peru, Spain are the rows; '50s, '60s, '70s, '80s are the columns. France and Spain are the European countries. How many stamps in the '80s column come from European countries?

Givens: European countries in the collection: France and Spain; From the '80s column: France has $15$ stamps, Spain has $9$ stamps; (Brazil $8$ and Peru $10$ in the '80s column are South American, so they do not count); Answer choices: (A) $9$, (B) $15$, (C) $18$, (D) $24$, (E) $42$

Unknowns: The total number of European stamps issued in the '80s

Understand

Plan

Primary tool: #1 Draw a Diagram

Secondary: #2 Make a Systematic List

The data already comes as a diagram — the country-by-decade table. Tool #1 (Draw a Diagram) here means "use the table as your diagram": find the right row and the right column, and read the cell at their intersection. Tool #2 (Make a Systematic List) keeps the lookup honest — list the European rows (France, Spain), pull the '80s entry from each, and add. With only two cells to read, this is the smallest possible tool set.

Execute — Answer: D

#1 Draw a Diagram 1.MD.C.4 Step 1

Locate the right column and the right rows in the table.
The '80s column is the rightmost.
The European rows are France and Spain (the introductory paragraph names them as the European countries).

$$\text{Target column: '80s} \quad ; \quad \text{Target rows: France, Spain}$$

💡 A table is a diagram with rows and columns. Knowing which row and which column to look at turns the problem into a single lookup.

#2 Make a Systematic List 1.MD.C.4 Step 2

List the European stamps from the '80s, one country at a time.
Reading the '80s column at the France row gives $15$, and at the Spain row gives $9$.

$$\text{France, '80s} = 15 \quad ; \quad \text{Spain, '80s} = 9$$

💡 A short, ordered list (France then Spain) makes sure no European row is missed and no non-European row sneaks in.

#2 Make a Systematic List 2.OA.A.1 Step 3

Add the two counts to get the total number of European stamps from the '80s.

$$15 + 9 = 24 \;\Rightarrow\; \textbf{(D)}$$

💡 Combining two counts into a total is a Grade 2 "add to find how many in all" word problem.

[1] #1 1.MD.C.4 Locate the right column and the right rows in the table. The '80s column is the

[2] #2 1.MD.C.4 List the European stamps from the '80s, one country at a time. Reading the '80s

[3] #2 2.OA.A.1 Add the two counts to get the total number of European stamps from the '80s.

Review

Reasonableness: Sanity-check by adding the full '80s column and subtracting the non-European entries. The '80s column reads $8$ (Brazil), $15$ (France), $10$ (Peru), $9$ (Spain), summing to $42$. The South American countries are Brazil ($8$) and Peru ($10$), totaling $18$. Then European $= 42 - 18 = 24$, matching (D). The two distractors fit common slips: $42$ is the whole '80s column, and $18$ is the South American total — both wrong for the question asked.

Alternative: Tool #3 (Eliminate Possibilities) on the answer list. The European countries in the '80s contribute at least $15$ (France alone), so (A) $9$ and (B) $15$ are too small ((B) would require Spain to have $0$, which it does not). The whole '80s column sums to $42$, so (E) is the entire column including South America — too large. That leaves (C) $18$ or (D) $24$. Adding $15 + 9 = 24$ picks (D).

CCSS standards used (min grade 2)

1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points and how many are in each category (Reading the two-way country-by-decade table to find the entries in the France and Spain rows under the '80s column.)
2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems (Adding the France '80s count ($15$) and the Spain '80s count ($9$) to get the European '80s total $24$.)

⭐ When a problem hands you a table, the table is your tool: pick the right rows (France, Spain) and the right column ('80s), read the cells ($15$ and $9$), and add — $15 + 9 = 24$, choice (D).

Problem

Toolkit + CCSS Solution

Understand

Plan

Execute — Answer: D

Review

CCSS standards used (min grade 2)

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