AMC 10 · 2021 · #4
Grade 5 logicPick an answer.
Five answer choices, all multiple-choice — Tool #3 (Eliminate Possibilities) tests each in turn against the three given facts. Tool #1 (Draw a Diagram) sketches the facts as arrows between properties so the chain is visible. Tool #7 (Identify Subproblems) splits the work: first chain facts 2 and 3, then bring in the contrapositive of fact 1, then read off which arrow lands on the answer.
Write the facts as arrows
Write the three facts as arrows.
An if-then statement is just an arrow from one property box to another.
5.G.B.3Draw A DiagramChain from purple
Purple chains to cannot add.
Arrow A→B and arrow B→C give a combined arrow A→C — like a transitive chain.
One arrow into a property and another out of it combine into a single arrow across both.
▸ Why?
An implication passes along a chain, so linking two of them carries the conclusion through.
▸ Why?
Everything inside the first group is inside the second, so it inherits whatever the second guarantees.
Reverse with the contrapositive
The contrapositive reverses the last arrow.
"All A are B" and "anything that is not B is not A" say the exact same thing.
5.G.B.3Identify SubproblemsComplete the chain
Purple now chains to not happy.
Combine two arrows then flip with the contrapositive to land on the answer's phrasing.
5.G.B.3Identify SubproblemsMatch the choice
The answer is happy snakes are not purple.
Walk down the five options and keep only the one that the chain forces.
5.G.B.3Eliminate PossibilitiesThis AMC 12 problem only needs Grade 5 category reasoning you already know — turn each "all A are B" into an arrow, chain purple → not-subtract → not-add and flip happy → can-add to its contrapositive, and the chain gives happy → not-purple, which is choice (D).