AMC 8 · 2011 · #6
Grade 4 arithmeticPick an answer.
AMC 8 2011 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The trigger words "car, motorcycle, or both" and "do not own a motorcycle" point straight at Tool #12 (Venn Diagram): two overlapping circles for Car and Motorcycle, with the every-adult-owns-at-least-one condition meaning the two circles cover all 351 adults (no "neither" region). The question "car owners who do not own a motorcycle" is the left-only slice of the Venn diagram, which is exactly Tool #16 (Count the Complement) — instead of counting the slice directly, compute the overlap first and subtract from the car total.
Draw overlapping circles C (cars) and M (motorcycles); since everyone owns one, C ∪ M holds all 351 adults with no outside region.
Draw the picture first: two circles inside one big box, and label what each region has to add up to.
4.OA.A.3Draw A Venn DiagramAdding the car and motorcycle totals double-counts the both-group, so the overlap is 331 + 45 - 351 = 25.
The center of the Venn diagram ("both") is whatever has been double-counted — the excess of C + M over the true total.
4.NBT.B.4Draw A Venn DiagramFlip to the complement: subtract the overlap from the car total to get car owners with no motorcycle: 331 - 25 = 306.
Inside the car circle there are two parts: "car + motorcycle" and "car only." Subtract the part we don't want from the whole.
4.NBT.B.4Count The Complement306 lands on choice (D).
The Venn-diagram bookkeeping lands exactly on one of the listed choices.
4.OA.A.3Draw A Venn DiagramThis AMC 8 problem is really a Grade 4 Venn-diagram puzzle: count the overlap, then take it away from the car circle.
More like this
Same archetype — closest grade level first.
