AMC 8 · 2017 · #2
Grade 6 rate-ratio
Pick an answer.
AMC 8 2017 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Because this is multiple-choice with only five candidate totals, we can take each choice T, compute 30% of it, and keep the one that gives exactly 36 votes. That is Tool #6 (Guess and Check) used directionally, combined with Tool #3 (Eliminate Possibilities), which is the AMC default whenever the answer is one of five listed numbers. No algebra is required: a Grade 6 student who can take 10% of a number can finish this problem mentally.
Brenda's labeled 30% slice equals her 36 real votes, so 30% of the total T must equal 36.
Reading a slice of a pie chart as "this percent of the whole" is the Grade 6 data-display skill — a labeled 30% slice simply means 30% of the total.
6.SP.B.5Eliminate PossibilitiesSince 10% of T is T/10, take 30% as 3 × T/10 — a quick mental check for each choice.
Computing a percent of a quantity is Grade 6 ratio-and-percent reasoning, and breaking 30% into "three tens" makes the check mental arithmetic.
6.RP.A.3Guess And CheckTesting (A)–(D): 30% of 70, 84, 100, 106 gives 21, 25.2, 30, 31.8 — none equals 36, so all four are eliminated.
Plugging each multiple-choice option back into the percent condition is the textbook "eliminate possibilities" move.
6.RP.A.3Eliminate PossibilitiesTesting (E): 30% of 120 is 3 × 12 = 36, matching Brenda's votes, so the total is 120.
The guess that matches the given 36 votes is the answer — guess-and-check on a finite list always terminates here.
6.RP.A.3Guess And CheckOnly T = 120 satisfies 30% × T = 36, so the answer is (E) 120.
Only one of the five listed totals matches the percent condition, and that's the answer we report.
6.RP.A.3Eliminate PossibilitiesThis AMC 8 problem only needs Grade 6 "percent of a number" you already know — just check which total makes 30% of it equal 36!