AMC 10 · 2020 · #1

Grade 7 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

multi-digit-arithmeticorder-of-operations pattern-recognitionidentify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 1 insight

Problem

Compute the value of 1-(-2)-3-(-4)-5-(-6).

Pick an answer.

(A)

-20

(B)

-3

(C)

(D)

(E)

AMC 10 2020 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Look for a Pattern

Tool #5 (Look for a Pattern): the signs alternate in a clean rhythm — every other term is “minus a negative,” which flips to “plus.” Spotting that pattern turns the scary-looking string into a simple add/subtract problem. Tool #15 (Reorganize) helps once the signs are fixed: group the positives and negatives separately so the arithmetic is just two small sums.

1STEP 1

Rewrite each 'minus a negative' as 'plus a positive', so the string becomes 1+2-3+4-5+6.

1-(-2)-3-(-4)-5-(-6) = 1+2-3+4-5+6

2STEP 2

Regroup the positives and negatives into two easy sums: 13 + (-8).

(1+2+4+6) + (-3-5) = 13 + (-8)

3STEP 3

Add them up: 13 + (-8) = 5, which is choice (D).

13 + (-8) = 5 → (D)

Answer

Recompute left-to-right without grouping: 1-(-2)=3; 3-3=0; 0-(-4)=4; 4-5=-1; -1-(-6)=5. Same answer, so (D) is correct.

💡Key takeaway

This AMC 10 problem only needs Grade 7 “subtracting a negative is adding a positive” you already know — the messy string is really 1+2-3+4-5+6 = 5.

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