AMC 8 · 2006 · #2

Grade 3 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Linear Rate Accumulation

mental-arithmeticmulti-digit-arithmeticif-then-reasoning identify-subproblems ↑ Prerequisites: multi-digit-arithmetic

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Problem

On the AMC 8, Billy gets 13 questions right, gets 7 wrong, and leaves the last 5 blank. Find his total score.

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 8 2006 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Analyze the Units

The unit on every question is "points". Each correct answer is worth 1 point and each non-correct answer (wrong or blank) is worth 0 points. Tool #8 (Analyze the Units) frames the question as a points-per-answer rate, which collapses everything to a single multiplication. Tool #7 (Identify Subproblems) splits the 25 questions into three buckets — correct, incorrect, blank — so the points from each bucket can be counted separately and then added. Two buckets contribute zero, so the score is just the count of correct answers.

1STEP 1

Sort the 25 answers into three buckets — correct, wrong, blank — where correct is worth 1 point and wrong and blank are worth 0.

correct: 13 answers × 1 pt | wrong: 7 × 0 | blank: 5 × 0

2STEP 2

Multiply each bucket by its rate and add: wrong and blank give 0, so the total is 13.

13 × 1 + 7 × 0 + 5 × 0 = 13 + 0 + 0 = 13 → (C)

Answer

Sanity check the totals: 13 + 7 + 5 = 25, which is exactly the number of questions on the AMC 8 — the buckets account for every answer, nothing double-counted. The score 13 also sits between the smallest possible non-zero score (1) and the maximum (25), so the magnitude is reasonable. Distractors hint at common mistakes: (D) 19 = 13 + 7 - 1 confuses penalty rules, (E) 26 = 13 × 2 doubles the correct count, (B) 6 = 13 - 7 subtracts wrong from right. The correct rule (wrong = 0, blank = 0) lands on (C).

💡Key takeaway

On the AMC 8, only correct answers add points — wrong and blank both score zero. So the total score is just the count of correct answers: 13.

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