Competition · AMC preparation · step 4 of 4

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

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?

Pick an answer.

(A)

(B)

(C)

(D)

(E)

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

How to solve

Strategy Draw a Diagram

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.

1STEP 1

Find the right row and column

The table is a diagram: the target column is the '80s (rightmost), and the European rows are France and Spain.

Target column: '80s ; Target rows: France, Spain

2STEP 2

List the European counts

Reading the '80s column: the France row gives 15 and the Spain row gives 9.

France, '80s = 15 ; Spain, '80s = 9

3STEP 3

Add the two counts

Add the two counts: 15 + 9 = 24, which is choice (D).

15 + 9 = 24 → (D)

Answer

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.

💡Key takeaway

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).

Find the right row and column
List the European counts
Add the two counts

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Find the right row and column

List the European counts

Add the two counts

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