AMC 8 · 2010 · #3

Grade 6 rate-ratio
Archetype Arithmetic Expression Decomposition └ Sub-archetype Weighted Group Aggregation
percentagegraph-readingfraction-arithmetic identify-subproblems ↑ Prerequisites: percentagemulti-digit-arithmetic
📏 Medium solution 💡 3 insights 📊 Diagram
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Problem
A bar graph shows the price of 5 gallons of gasoline for each of the first 10 months of the year. Reading the bars, the highest price is 17</span>(Month1)and<spanclass="mk−c">thelowestpriceis17</span> (Month 1) and <span class="mk-c">the lowest price is10 (Month 3). By what percent does the highest price exceed the lowest price?

Pick an answer.

(A)
50
(B)
62
(C)
70
(D)
89
(E)
100

AMC 8 2010 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Look for a Pattern

The problem has a simple shape — read two numbers off the graph, then compute a percent increase — so the work splits cleanly into Tool #7 subproblems: (1) extract the maximum and minimum from the bar chart, (2) compute the percent increase using high−lowlow\frac{high - low}{low} × 100%. Tool #5 (Look for a Pattern) is what makes the second step quick: 7onabaseof7 on a base of10 is the familiar pattern 710\frac{7}{10} = 0.70 = 70%, so no long division is needed.

1STEP 1

Scan all ten bars: Month 1 is the tallest at the 17</span></span>level,Month3theshortestatthe<spanclass="mk−a"><spanclass="hl−ask">17</span></span> level, Month 3 the shortest at the <span class="mk-a"><span class="hl-ask">10 gridline.

highest = 17,lowest=17, lowest =10
2STEP 2

The gap between the two prices is $7 — how much the high price clears the low.

17−17 -10 = $7
3STEP 3

"Exceeds by what percent" means divide the gap by the lowest price — the base — then scale to a percent.

percent more = $17−$10$10\frac{\$17 - \$10}{\$10} × 100% = $7$10\frac{\$7}{\$10} × 100%
4STEP 4

The fraction 710\frac{7}{10} is exactly 0.7, so the high price is 70% more than the low.

710\frac{7}{10} × 100% = 70% → (C)
Answer
70
If the high price were double the low price, the increase would be 100%; doubling 10wouldmeanahighof10 would mean a high of20. Since 17isbelow17 is below20 but well above 10,theanswermustbelessthan10010, the answer must be less than 100% but more than 50%. That rules out (A) and (E) and leaves (B) 62, (C) 70, (D) 89. Our calculation\frac{7}{10}$ = 70% lands on (C), which sits in the expected window.
💡Key takeaway

This AMC 8 problem only needs Grade 6 percent reasoning — divide the gap by the smaller number — that you already know!

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