5 questions: Q10, Q11, Q12, Q13, Q14. Solve each one here: tap the answer, press Check, then open the solution.
DI/DS
The set
SET 3: ARENA FIGHTERS – SURVIVAL BY COIN BRACKET A study began in 1980 to determine the retention rate of Arena fighters. It selected 1000 male fighters and 1000 female fighters and followed them until they retired. In 1980, each gender had 250 fighters in each of the following coin brackets: 10 to less than 20, 20 to less than 30, 30 to less than 40, and 40 to less than 50. The accompanying bar graph shows the number of male and female fighters still active in the Arena in 1990, 2000, 2010 and 2020, across the coin brackets shown. A fighter's coin bracket increases by exactly 10 for every 10 years. For example, a fighter in the 20–30 bracket in 1980 moves to the 40–50 bracket in 2000.
How many individuals who were being tracked and who had less than 30 coins in 1980 remained active until 2020?
Refer to the bar graph provided with this set.
Answer and solution
Correct answer: D
Solution
Answer: D — 470
1. The starting cohorts below 30 are 10–20 and 20–30 in 1980. 2. Forty years add 40 coins, moving these cohorts to 50–60 and 60–70 in 2020. 3. Read the orange and pale-orange bars, not the other year colours: 50–60 has 140 males and 100 females; 60–70 has 125 males and 105 females. 4. Add both genders across both cohorts: 140+100+125+105=470. 5. Answer: D, 470. 6. Track a cohort diagonally through the chart: add 10 to its bracket for each decade, rather than comparing the same bracket across years.
Detailed setup and verification: The phrase less than 30 refers to the starting year 1980. There were two eligible brackets, each with 250 members of each gender. Move those same cohorts forward 40 years before reading the graph. The labels 50–60 and 60–70 in 2020 identify them; the chart’s youngest brackets do not.
As a cross-check, male survivors in the two target brackets total 265 and female survivors total 205. Their combined 470 agrees with adding all four bars. This is a surviving count, so do not subtract it from the initial 1000 eligible fighters.
G Strategy shortcut
Method: 1980 under 30 becomes 2020 brackets 50–60 and 60–70. Add 140+100+125+105=470. Verification: 1. The starting cohorts below 30 are 10–20 and 20–30 in 1980. 2. Forty years add 40 coins, moving these cohorts to 50–60 and 60–70 in 2020. 3. Read the orange and pale-orange bars, not the other year colours: 50–60 has 140 males and 100 females; 60–70 has 125 males and 105 females. 4. Add both genders across both cohorts: 140+100+125+105=470. 5. Answer: D, 470. 6. Track a cohort diagonally through the chart: add 10 to its bracket for each decade, rather than comparing the same bracket across years. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: 1980 under 30 becomes 2020 brackets 50–60 and 60–70. Add 140+100+125+105=470.
Verification: 1. The starting cohorts below 30 are 10–20 and 20–30 in 1980.
2. Forty years add 40 coins, moving these cohorts to 50–60 and 60–70 in 2020.
3. Read the orange and pale-orange bars, not the other year colours: 50–60 has 140 males and 100 females; 60–70 has 125 males and 105 females.
4. Add both genders across both cohorts: 140+100+125+105=470.
5. Answer: D, 470.
6. Track a cohort diagonally through the chart: add 10 to its bracket for each decade, rather than comparing the same bracket across years.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
How many female fighters who were in the 20 to less than 30 coin bracket in 1980 retired between the 2010 and 2020 observations?
Refer to the bar graph provided with this set.
Answer and solution
Correct answer: 40
Solution
Answer: 40
1. Track the same cohort over time, rather than comparing one fixed coin bracket.
2. A female fighter in bracket 20–30 in 1980 is in bracket 50–60 in 2010 and 60–70 in 2020.
3. The graph gives 145 active female fighters for the first observation and 105 for the second.
4. Retirements between the observations=145−105=40. The value 30 belongs to 2000–2010 and is not the interval now asked.
Detailed setup and verification: Draw a four-decade chain for this female cohort:20–30 in 1980,30–40 in 1990,40–50 in 2000,50–60 in 2010 and 60–70 in 2020. The relevant 2010 and 2020 bars are purple-light and pale orange, respectively.
A cohort is a fixed group: its fall from 145 active fighters to 105 means 40 retirements during that interval. The percentage retired would be 40/145, but the question asks for a number, so no division or percent sign belongs in the answer.
G Strategy shortcut
Method: Follow the cohort diagonally: 1980 bracket 20–30 →2010 bracket 50–60 →2020 bracket 60–70. Subtract 145−105=40. Verification: 4. Retirements between the observations=145−105=40. The value 30 belongs to 2000–2010 and is not the interval now asked. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: Follow the cohort diagonally: 1980 bracket 20–30 →2010 bracket 50–60 →2020 bracket 60–70. Subtract 145−105=40.
Verification: 4. Retirements between the observations=145−105=40. The value 30 belongs to 2000–2010 and is not the interval now asked.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
In 2000, what was the ratio of the number of retired male fighters to retired female fighters among those being tracked?
Refer to the bar graph provided with this set.
Answer and solution
Correct answer: C
Solution
Answer: C — 71 : 69
1. Each gender begins with 1000 fighters. 2. In 2000 sum male bars across 30–40,40–50,50–60,60–70: 180+205+160+100=645. 3. Male retirements are 1000−645=355. Female survivors are 210+175+150+120=655, giving 345 retirements. 4. Form the requested male: female ratio 355:345 and divide both terms by 5. 5. Answer: C, 71:69.
Detailed setup and verification: The required quantity is retired fighters, whereas the bars show active fighters. First sum all 2000 active bars separately by gender; only then subtract each from its own initial 1000. Combining genders first would lose the information needed for the ratio.
Male check: 645 active+355 retired=1000. Female check: 655 active+345 retired=1000. The ratio is retired male:retired female, so 355:345=71:69; reversing it gives 69:71 and comparing active totals gives 129:131, a distractor.
G Strategy shortcut
Method: 2000 survivors 645 M, 655 F; retirements 355M,345F →71:69. Verification: 1. Each gender begins with 1000 fighters. 2. In 2000 sum male bars across 30–40,40–50,50–60,60–70: 180+205+160+100=645. 3. Male retirements are 1000−645=355. Female survivors are 210+175+150+120=655, giving 345 retirements. 4. Form the requested male: female ratio 355:345 and divide both terms by 5. 5. Answer: C, 71:69. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: 2000 survivors 645 M, 655 F; retirements 355M,345F →71:69.
Verification: 1. Each gender begins with 1000 fighters.
2. In 2000 sum male bars across 30–40,40–50,50–60,60–70: 180+205+160+100=645.
3. Male retirements are 1000−645=355. Female survivors are 210+175+150+120=655, giving 345 retirements.
4. Form the requested male: female ratio 355:345 and divide both terms by 5.
5. Answer: C, 71:69.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
How many of the male fighters who were being tracked and who had 20 to less than 30 coins in 1980 retired in the period 2000 to 2010?
Refer to the bar graph provided with this set.
Answer and solution
Correct answer: 40
Solution
Answer: 40
1. The original 20–30 male cohort becomes 40–50 in 2000 and 50–60 in 2010. 2. Read the 2000 male green bar at 40–50: 205. 3. Read the 2010 male purple bar at 50–60: 165. 4. The decrease in active tracked members is 205−165=40; no new fighters enter the tracked cohort. 5. Answer: 40.
Detailed setup and verification: Use the male series and keep the initial cohort fixed. The 2000 count 205 is not compared with the 2010 bar at 40–50; the fighters themselves have moved up one bracket, so the correct 2010 count is 165 at 50–60.
The difference 205−165=40 is the number who retired during the interval. The starting 1980 count 250 would be needed for cumulative retirements since 1980, but the question starts its interval at 2000, so subtracting from 250 would answer a different question.
G Strategy shortcut
Method: Same cohort: 2000 male 40–50=205;2010 male 50–60=165. Difference 40. Verification: 1. The original 20–30 male cohort becomes 40–50 in 2000 and 50–60 in 2010. 2. Read the 2000 male green bar at 40–50: 205. 3. Read the 2010 male purple bar at 50–60: 165. 4. The decrease in active tracked members is 205−165=40; no new fighters enter the tracked cohort. 5. Answer: 40. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: Same cohort: 2000 male 40–50=205;2010 male 50–60=165. Difference 40.
Verification: 1. The original 20–30 male cohort becomes 40–50 in 2000 and 50–60 in 2010.
2. Read the 2000 male green bar at 40–50: 205.
3. Read the 2010 male purple bar at 50–60: 165.
4. The decrease in active tracked members is 205−165=40; no new fighters enter the tracked cohort.
5. Answer: 40.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
How many fighters who were being tracked and who had 30 to less than 40 coins in 1980 remained active until 2010?
Refer to the bar graph provided with this set.
Answer and solution
Correct answer: D
Solution
Answer: D — 190
1. The starting bracket is 30–40 in 1980. 2. Thirty years add 30 coins, so find 60–70 in 2010. 3. Read the 2010 male and female bars: 90 and 100 respectively. 4. Combine the two genders: 90+100=190. Do not use the 2010 bracket 30–40 or the 2020 bars. 5. Answer: D, 190.
Detailed setup and verification: This is one cohort and both genders. Starting 30–40 in 1980 becomes 60–70 in 2010 because 30 years have elapsed. Read only the 2010 male/female pair at that bracket: 90 and 100.
The result 190 is at most the cohort’s initial 500 fighters, as it should be. The other chart values 110 and 310 can arise from unrelated years or brackets; use the year, cohort and gender filters before doing any arithmetic.
G Strategy shortcut
Method: 1980 bracket 30–40 shifts to 2010 bracket 60–70: 90M+100F=190. Verification: 1. The starting bracket is 30–40 in 1980. 2. Thirty years add 30 coins, so find 60–70 in 2010. 3. Read the 2010 male and female bars: 90 and 100 respectively. 4. Combine the two genders: 90+100=190. Do not use the 2010 bracket 30–40 or the 2020 bars. 5. Answer: D, 190. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: 1980 bracket 30–40 shifts to 2010 bracket 60–70: 90M+100F=190.
Verification: 1. The starting bracket is 30–40 in 1980.
2. Thirty years add 30 coins, so find 60–70 in 2010.
3. Read the 2010 male and female bars: 90 and 100 respectively.
4. Combine the two genders: 90+100=190. Do not use the 2010 bracket 30–40 or the 2020 bars.
5. Answer: D, 190.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
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