GRE Multi-Step Data Analysis and Graphs 1 — Questions and Answers
Question 1: A company's annual revenue (in millions) over five years was: Year 1: $120M, Year 2: $144M, Year 3: $172.8M, Year 4: $207.4M, Year 5: $248.8M. What was the approximate average percentage growth rate per year? (A) 15% (B) 18% (C) 20% (D) 22%
- 15%
- 18%
- 20% (Correct answer)
- 22%
Correct answer: 20%
Each year the revenue grows by exactly 20%: 120 × 1.2 = 144, 144 × 1.2 = 172.8, etc. The answer is 20%.
Year 1 to 2: 144/120 = 1.20 (20% growth). Year 2 to 3: 172.8/144 = 1.20. Year 3 to 4: 207.4/172.8 ≈ 1.20. Year 4 to 5: 248.8/207.4 ≈ 1.20. The growth rate is consistently 20% each year.
Question 2: A bar chart shows quarterly sales for two products: Product A: Q1=40, Q2=55, Q3=70, Q4=85 (units) Product B: Q1=80, Q2=70, Q3=60, Q4=50 (units) In which quarter does the combined total first exceed 120 units? (A) Q1 (B) Q2 (C) Q3 (D) Q4
- Q1
- Q2 (Correct answer)
- Q3
- Q4
Correct answer: Q2
Q1: 40+80=120 (not exceeding). Q2: 55+70=125 > 120. The combined total first exceeds 120 in Q2.
Q1: 40 + 80 = 120 (equals but does not exceed). Q2: 55 + 70 = 125 > 120. Q3: 70 + 60 = 130. Q4: 85 + 50 = 135. The first quarter where the combined total exceeds 120 is Q2.
Question 3: A pie chart shows the distribution of 360 survey respondents by preferred news source: TV = 30%, Online = 45%, Print = 15%, Radio = 10%. How many more respondents prefer Online compared to the combined total of Print and Radio? (A) 54 (B) 72 (C) 81 (D) 90
- 54
- 72 (Correct answer)
- 81
- 90
Correct answer: 72
Online: 45% × 360 = 162. Print + Radio: (15% + 10%) × 360 = 25% × 360 = 90. Difference: 162 − 90 = 72.
Online: 0.45 × 360 = 162 respondents. Print: 0.15 × 360 = 54. Radio: 0.10 × 360 = 36. Print + Radio = 54 + 36 = 90. 162 − 90 = 72 more respondents prefer Online over the combined Print and Radio total.
Question 4: A line graph shows a city's population (in thousands) from 2000 to 2020 in 5-year intervals: 2000=200, 2005=230, 2010=272, 2015=306, 2020=340. Between which two 5-year periods was the absolute increase in population the greatest? (A) 2000–2005 (B) 2005–2010 (C) 2010–2015 (D) 2015–2020
- 2000–2005
- 2005–2010 (Correct answer)
- 2010–2015
- 2015–2020
Correct answer: 2005–2010
Increases: 2000–05: 30K; 2005–10: 42K; 2010–15: 34K; 2015–20: 34K. The 2005–2010 period had the largest absolute increase of 42,000.
2000–2005: 230 − 200 = 30 thousand. 2005–2010: 272 − 230 = 42 thousand. 2010–2015: 306 − 272 = 34 thousand. 2015–2020: 340 − 306 = 34 thousand. The greatest absolute increase was 42,000 during 2005–2010.
Question 5: A table shows test scores for two classes: Class A: Mean = 78, Standard Deviation = 5, n = 30 Class B: Mean = 82, Standard Deviation = 12, n = 20 Which class had greater score variability, and by approximately what factor? (A) Class A; variability 2.4 times greater (B) Class B; variability 2.4 times greater (C) Class A; variability 1.5 times greater (D) Class B; variability 1.5 times greater
- Class A; variability 2.4 times greater
- Class B; variability 2.4 times greater (Correct answer)
- Class A; variability 1.5 times greater
- Class B; variability 1.5 times greater
Correct answer: Class B; variability 2.4 times greater
Standard deviation measures variability. Class B: SD=12; Class A: SD=5. 12/5 = 2.4. Class B had 2.4× greater variability.
Standard deviation is the measure of variability in this context. Class B has SD = 12, Class A has SD = 5. The ratio is 12 ÷ 5 = 2.4. Therefore, Class B's scores were 2.4 times more variable than Class A's.
Question 6: A scatterplot shows the relationship between hours studied per week (x-axis, range 0–20) and exam score (y-axis, range 40–100). The best-fit line has the equation y = 3x + 50. A student studies 15 hours per week. What score does the model predict, and how does it compare to a student who studies 10 hours? (A) Predicts 95; 15 points higher than the 10-hour student (B) Predicts 95; 10 points higher than the 10-hour student (C) Predicts 100; 20 points higher than the 10-hour student (D) Predicts 90; 20 points higher than the 10-hour student
- Predicts 95; 15 points higher than the 10-hour student (Correct answer)
- Predicts 95; 10 points higher than the 10-hour student
- Predicts 100; 20 points higher than the 10-hour student
- Predicts 90; 20 points higher than the 10-hour student
Correct answer: Predicts 95; 15 points higher than the 10-hour student
15 hours: y = 3(15) + 50 = 95. 10 hours: y = 3(10) + 50 = 80. Difference: 95 − 80 = 15 points.
For 15 hours: y = 3(15) + 50 = 45 + 50 = 95. For 10 hours: y = 3(10) + 50 = 30 + 50 = 80. The 15-hour student scores 95, which is 95 − 80 = 15 points higher than the 10-hour student.
Question 7: A table shows monthly electricity costs for an office building: Jan–Mar (avg): $1,200/month Apr–Jun (avg): $900/month Jul–Sep (avg): $1,500/month Oct–Dec (avg): $1,050/month What is the total annual electricity cost? (A) $13,800 (B) $13,950 (C) $14,100 (D) $14,400
- $13,800 (Correct answer)
- $13,950
- $14,100
- $14,400
Correct answer: $13,800
Each average applies to 3 months: (1200×3) + (900×3) + (1500×3) + (1050×3) = 3600 + 2700 + 4500 + 3150 = $13,950.
Jan–Mar: $1,200 × 3 = $3,600. Apr–Jun: $900 × 3 = $2,700. Jul–Sep: $1,500 × 3 = $4,500. Oct–Dec: $1,050 × 3 = $3,150. Total: $3,600 + $2,700 + $4,500 + $3,150 = $13,950. The correct answer is (B) $13,950.
Question 8: A double bar chart compares men's and women's marathon finish times (in minutes) across 4 age groups: Age 20–29: Men=210, Women=235 Age 30–39: Men=215, Women=242 Age 40–49: Men=225, Women=255 Age 50–59: Men=240, Women=275 In which age group is the absolute difference between men's and women's times the greatest? (A) 20–29 (B) 30–39 (C) 40–49 (D) 50–59
- 20–29
- 30–39
- 40–49
- 50–59 (Correct answer)
Correct answer: 50–59
Differences: 20–29: 25min; 30–39: 27min; 40–49: 30min; 50–59: 35min. The 50–59 age group has the greatest difference.
20–29: 235 − 210 = 25 minutes. 30–39: 242 − 215 = 27 minutes. 40–49: 255 − 225 = 30 minutes. 50–59: 275 − 240 = 35 minutes. The greatest absolute difference is 35 minutes in the 50–59 age group.
Question 9: An investment portfolio had the following returns over 4 years: Year 1: +20%, Year 2: −10%, Year 3: +25%, Year 4: −5%. What was the approximate net percentage change over all 4 years? (A) +23% (B) +28% (C) +30% (D) +35%
- +23%
- +28% (Correct answer)
- +30%
- +35%
Correct answer: +28%
Net return = 1.20 × 0.90 × 1.25 × 0.95 = 1.08 × 1.25 × 0.95 = 1.35 × 0.95 = 1.2825 ≈ 28.25% gain.
Convert each return to a multiplier: 1.20, 0.90, 1.25, 0.95. Multiply: 1.20 × 0.90 = 1.08; 1.08 × 1.25 = 1.35; 1.35 × 0.95 = 1.2825. This means the portfolio grew to 128.25% of its original value — a net gain of approximately 28.25%, closest to 28%.
Question 10: A histogram shows the distribution of test scores for 100 students: 50–59: 5 students 60–69: 15 students 70–79: 35 students 80–89: 30 students 90–99: 15 students What percentage of students scored below 80? (A) 45% (B) 50% (C) 55% (D) 60%
- 45%
- 50%
- 55% (Correct answer)
- 60%
Correct answer: 55%
Students below 80: 5 + 15 + 35 = 55. 55/100 = 55%.
Score ranges below 80 are 50–59 (5), 60–69 (15), and 70–79 (35). Total below 80: 5 + 15 + 35 = 55 students. Percentage: 55/100 × 100% = 55%.
Question 11: A two-way table shows survey results on coffee preference by age group: Under 30: Coffee=40, Tea=60, Total=100 Over 30: Coffee=90, Tea=60, Total=150 Total: Coffee=130, Tea=120, Grand Total=250 What percentage of coffee drinkers are over 30? (A) 60% (B) 65% (C) 69% (D) 72%
- 60%
- 65%
- 69% (Correct answer)
- 72%
Correct answer: 69%
Coffee drinkers over 30: 90. Total coffee drinkers: 130. 90/130 ≈ 0.692 = 69.2% ≈ 69%.
Total coffee drinkers = 130. Coffee drinkers over 30 = 90. Proportion: 90 ÷ 130 = 0.6923... ≈ 69%. This is a conditional probability: P(over 30 | coffee drinker) = 90/130.
Question 12: A stacked bar chart shows the composition of a city's workforce (1,000 workers total): Government 25%, Private sector 55%, Self-employed 15%, Other 5%. If the workforce grows by 20% next year with all proportions staying the same, how many more private sector workers will there be? (A) 100 (B) 110 (C) 120 (D) 130
- 100
- 110 (Correct answer)
- 120
- 130
Correct answer: 110
Current private sector: 55% × 1000 = 550. New total: 1200. New private sector: 55% × 1200 = 660. Increase: 660 − 550 = 110.
Current workforce = 1,000. Private sector = 55% × 1,000 = 550 workers. New workforce = 1,000 × 1.20 = 1,200. New private sector = 55% × 1,200 = 660. Increase = 660 − 550 = 110 additional private sector workers.
Question 13: A line graph shows two companies' quarterly profits (in $M): Company X: Q1=10, Q2=14, Q3=19, Q4=25 Company Y: Q1=22, Q2=20, Q3=18, Q4=15 In which quarter do the lines intersect (i.e., Company X's profit first equals or exceeds Company Y's)? (A) Q2 (B) Q3 (C) Q4 (D) They never intersect within the given data
- Q2
- Q3
- Q4 (Correct answer)
- They never intersect within the given data
Correct answer: Q4
Q1: X=10 < Y=22. Q2: X=14 < Y=20. Q3: X=19 > Y=18. Actually X first exceeds Y at Q3. But wait: we need when X first equals OR exceeds Y. At Q3, X=19 > Y=18, so Q3 is correct.
Q1: X=10, Y=22 → X < Y. Q2: X=14, Y=20 → X < Y. Q3: X=19, Y=18 → X > Y. Company X first exceeds Company Y in Q3. The lines cross between Q2 and Q3. Answer (B) Q3 is correct.
Question 14: A table shows the number of defective items per 1,000 produced at three factories over two years: Factory A: Year 1=25, Year 2=18 Factory B: Year 1=40, Year 2=28 Factory C: Year 1=15, Year 2=12 Which factory achieved the greatest percentage reduction in defects? (A) Factory A (B) Factory B (C) Factory C (D) Factories A and B tied
- Factory A
- Factory B (Correct answer)
- Factory C
- Factories A and B tied
Correct answer: Factory B
A: (25−18)/25 = 28% reduction. B: (40−28)/40 = 30% reduction. C: (15−12)/15 = 20% reduction. Factory B had the greatest percentage reduction at 30%.
Factory A: (25 − 18)/25 = 7/25 = 28% reduction. Factory B: (40 − 28)/40 = 12/40 = 30% reduction. Factory C: (15 − 12)/15 = 3/15 = 20% reduction. Despite reducing defects by the largest absolute number (12), Factory B also leads in percentage reduction at 30%.
Question 15: A graph shows that a city's carbon emissions (in million tons) follow the equation E = −0.4t + 12, where t = years after 2000. According to this model, in what year will emissions reach zero? (A) 2025 (B) 2028 (C) 2030 (D) 2032
- 2025
- 2028
- 2030 (Correct answer)
- 2032
Correct answer: 2030
Set E = 0: 0 = −0.4t + 12 → 0.4t = 12 → t = 30. Year 2000 + 30 = 2030.
−0.4t + 12 = 0. Subtract 12 from both sides: −0.4t = −12. Divide by −0.4: t = 30. Since t represents years after 2000, the year is 2000 + 30 = 2030.
Question 16: A pie chart shows that a school's budget is divided as follows: Instruction 48%, Administration 18%, Facilities 14%, Technology 12%, Other 8%. The total budget is $5 million. How much more is spent on Instruction than on Administration and Technology combined? (A) $800,000 (B) $900,000 (C) $1,000,000 (D) $1,200,000
- $800,000
- $900,000
- $1,000,000 (Correct answer)
- $1,200,000
Correct answer: $1,000,000
Instruction: 48% × $5M = $2.4M. Admin + Tech: (18%+12%) × $5M = 30% × $5M = $1.5M. Difference: $2.4M − $1.5M = $0.9M = $900,000.
Instruction = 0.48 × $5,000,000 = $2,400,000. Administration = 0.18 × $5,000,000 = $900,000. Technology = 0.12 × $5,000,000 = $600,000. Admin + Tech = $900,000 + $600,000 = $1,500,000. Difference = $2,400,000 − $1,500,000 = $900,000.
Question 17: A scatter plot shows data points that suggest a strong positive correlation between advertising spend and sales revenue. The correlation coefficient is r = 0.92. What does this tell us? (A) Advertising spending causes higher sales (B) About 85% of the variance in sales is explained by advertising spend (C) For every $1 increase in advertising, sales increase by exactly $0.92 (D) The relationship is linear and perfectly predictable
- Advertising spending causes higher sales
- About 85% of the variance in sales is explained by advertising spend (Correct answer)
- For every $1 increase in advertising, sales increase by exactly $0.92
- The relationship is linear and perfectly predictable
Correct answer: About 85% of the variance in sales is explained by advertising spend
r² = 0.92² ≈ 0.846. About 84.6% ≈ 85% of the variance in sales is explained by advertising spend. Correlation does not imply causation.
r = 0.92 means strong positive correlation. r² = 0.92² = 0.8464, meaning about 84.6% of variance in sales is explained by advertising spend. Option A is wrong — correlation does not prove causation. Option C confuses r with regression slope. Option D is wrong — r=1 would be perfect, not 0.92.
Question 18: A table shows the number of applications and acceptances at a university over 3 years: Year 1: Applications=8,000, Acceptances=1,200 Year 2: Applications=9,500, Acceptances=1,330 Year 3: Applications=11,000, Acceptances=1,430 In which year was the acceptance rate highest? (A) Year 1 (B) Year 2 (C) Year 3 (D) All years had the same acceptance rate
- Year 1 (Correct answer)
- Year 2
- Year 3
- All years had the same acceptance rate
Correct answer: Year 1
Year 1: 1200/8000 = 15%. Year 2: 1330/9500 ≈ 14%. Year 3: 1430/11000 = 13%. Year 1 had the highest acceptance rate.
Year 1: 1,200 ÷ 8,000 = 0.15 = 15%. Year 2: 1,330 ÷ 9,500 ≈ 0.14 = 14%. Year 3: 1,430 ÷ 11,000 ≈ 0.13 = 13%. Although absolute acceptances increased each year, the rate decreased because applications grew faster than acceptances.
Question 19: A graph shows exponential population growth modeled by P = 500 × 2^(t/10), where t = years. What is the population at t = 30? (A) 2,000 (B) 3,000 (C) 4,000 (D) 6,000
- 2,000
- 3,000
- 4,000 (Correct answer)
- 6,000
Correct answer: 4,000
P = 500 × 2^(30/10) = 500 × 2^3 = 500 × 8 = 4,000.
P = 500 × 2^(t/10). At t = 30: P = 500 × 2^(30/10) = 500 × 2^3 = 500 × 8 = 4,000. The population doubles every 10 years (t=0: 500; t=10: 1,000; t=20: 2,000; t=30: 4,000).
Question 20: A frequency table shows the grades of 40 students: A=8, B=14, C=12, D=4, F=2. What is the probability that a randomly selected student earned either a B or C? (A) 0.55 (B) 0.60 (C) 0.65 (D) 0.70
- 0.55
- 0.60
- 0.65 (Correct answer)
- 0.70
Correct answer: 0.65
B + C = 14 + 12 = 26. P = 26/40 = 0.65.
Students with B or C: 14 + 12 = 26. Total students: 40. P(B or C) = 26/40 = 0.65. This uses the addition rule for mutually exclusive events: P(B or C) = P(B) + P(C) = 14/40 + 12/40 = 26/40.
Question 21: A stacked line graph shows three regions' share of global renewable energy production over time. In 2015, Region A=40%, Region B=35%, Region C=25%. By 2020, Region A=35%, Region B=40%, Region C=25%. If total production was 2,000 TWh in 2015 and 3,000 TWh in 2020, how much more energy did Region B produce in 2020 vs. 2015? (A) 500 TWh (B) 520 TWh (C) 600 TWh (D) 700 TWh
- 500 TWh (Correct answer)
- 520 TWh
- 600 TWh
- 700 TWh
Correct answer: 500 TWh
Region B in 2015: 35% × 2000 = 700 TWh. Region B in 2020: 40% × 3000 = 1200 TWh. Increase: 1200 − 700 = 500 TWh.
2015: Region B = 35% × 2,000 TWh = 700 TWh. 2020: Region B = 40% × 3,000 TWh = 1,200 TWh. Increase = 1,200 − 700 = 500 TWh. Despite Region A losing share, Region B gained both in percentage and in total volume.
Question 22: A box-and-whisker plot for a dataset shows: minimum=20, Q1=35, median=50, Q3=70, maximum=95. What is the interquartile range (IQR), and what does it represent? (A) IQR=45; the range of the entire dataset (B) IQR=35; the spread of the middle 50% of data (C) IQR=30; the average distance from the mean (D) IQR=75; the distance from min to max
- IQR=45; the range of the entire dataset
- IQR=35; the spread of the middle 50% of data (Correct answer)
- IQR=30; the average distance from the mean
- IQR=75; the distance from min to max
Correct answer: IQR=35; the spread of the middle 50% of data
IQR = Q3 − Q1 = 70 − 35 = 35. The IQR represents the spread of the middle 50% of the data.
IQR = Q3 − Q1 = 70 − 35 = 35. The IQR is the range of the middle 50% of values (from the 25th percentile to the 75th percentile). The full range is max − min = 95 − 20 = 75. The IQR is more robust than the full range because it is not affected by extreme outliers.
Question 23: A comparative table shows the fuel efficiency (mpg) of 5 car models in city and highway driving: Model A: City=22, Highway=30 Model B: City=18, Highway=25 Model C: City=35, Highway=42 Model D: City=28, Highway=35 Model E: City=15, Highway=20 If a driver spends 60% of miles on the highway and 40% in the city, which model gives the best weighted average mpg? (A) Model A (B) Model C (C) Model D (D) Model E
- Model A
- Model C (Correct answer)
- Model D
- Model E
Correct answer: Model C
Weighted avg = 0.4(city) + 0.6(highway). C: 0.4(35)+0.6(42) = 14+25.2 = 39.2. All others are lower. Model C wins.
Model A: 0.4(22) + 0.6(30) = 8.8 + 18 = 26.8. Model B: 0.4(18) + 0.6(25) = 7.2 + 15 = 22.2. Model C: 0.4(35) + 0.6(42) = 14 + 25.2 = 39.2. Model D: 0.4(28) + 0.6(35) = 11.2 + 21 = 32.2. Model E: 0.4(15) + 0.6(20) = 6 + 12 = 18. Model C has the highest weighted average at 39.2 mpg.
Question 24: A bar chart shows annual revenue growth rates for a company: Year 1: 5%, Year 2: 8%, Year 3: −3%, Year 4: 12%, Year 5: 6%. If Year 1 starting revenue was $100M, what was the revenue at the end of Year 5? (A) $128M (B) $131M (C) $133M (D) $136M
- $128M
- $131M
- $133M (Correct answer)
- $136M
Correct answer: $133M
100 × 1.05 × 1.08 × 0.97 × 1.12 × 1.06 = 100 × 1.3326 ≈ $133M.
Year 1: 100 × 1.05 = 105. Year 2: 105 × 1.08 = 113.4. Year 3: 113.4 × 0.97 = 110.0. Year 4: 110.0 × 1.12 = 123.2. Year 5: 123.2 × 1.06 = 130.6. Wait: let me recalculate precisely: 100 × 1.05 = 105; ×1.08 = 113.4; ×0.97 = 110.0; ×1.12 = 123.2; ×1.06 = 130.6 ≈ $131M. Answer is (B) $131M.
Question 25: A graph shows that a city's water usage (gallons per person per day) decreased from 180 to 135 over 10 years. What was the percentage decrease? (A) 20% (B) 25% (C) 30% (D) 33%
- 20%
- 25% (Correct answer)
- 30%
- 33%
Correct answer: 25%
% decrease = (180 − 135)/180 × 100 = 45/180 × 100 = 25%.
(180 − 135) / 180 = 45 / 180 = 0.25 = 25%. The city reduced per-person water usage by 25% over the decade.
Question 26: A data table shows the results of a clinical trial: Treatment Group: 200 patients, 160 improved Control Group: 200 patients, 120 improved What is the relative risk reduction (RRR) of the treatment compared to control? (A) 20% (B) 25% (C) 33% (D) 40%
- 20%
- 25%
- 33% (Correct answer)
- 40%
Correct answer: 33%
Control improvement rate: 120/200 = 60%. Treatment improvement rate: 160/200 = 80%. RRR = (treatment rate − control rate)/control rate = (80%−60%)/60% = 20/60 ≈ 33%.
Control rate = 120/200 = 0.60 = 60%. Treatment rate = 160/200 = 0.80 = 80%. Absolute risk reduction = 80% − 60% = 20%. Relative risk reduction = 20% / 60% = 1/3 ≈ 33.3%.
Question 27: A frequency histogram has 5 bins of width 10: [10,20): 4, [20,30): 8, [30,40): 12, [40,50): 6, [50,60): 2. What is the approximate median of this data set (32 total observations)? (A) 28 (B) 32 (C) 35 (D) 38
- 28
- 32
- 35 (Correct answer)
- 38
Correct answer: 35
Cumulative: by 30 we have 4+8=12 values (37.5%). By 40 we have 12+12=24 (75%). The 16th and 17th values (median of 32) fall in [30,40). Estimate: 30 + ((16−12)/12)×10 = 30 + 3.3 ≈ 33. Closest answer is 35.
32 observations → median is average of 16th and 17th values. Cumulative counts: up to 20: 4; up to 30: 12; up to 40: 24. Both the 16th and 17th values fall in [30, 40). Interpolating: 30 + ((16−12)/12) × 10 = 30 + 3.33 ≈ 33. Of the choices given, 35 is the closest reasonable estimate.
Question 28: A table shows the average monthly temperature (°C) and ice cream sales (units) for 6 months: Temp: 10, 15, 20, 25, 30, 35 Sales: 200, 350, 500, 650, 800, 950 Which equation best models the relationship? (A) Sales = 30 × Temperature − 100 (B) Sales = 25 × Temperature + 200 (C) Sales = 30 × Temperature − 100 (D) Sales = 20 × Temperature + 200
- Sales = 30 × Temperature − 100 (Correct answer)
- Sales = 25 × Temperature + 200
- Sales = 30 × Temperature − 100
- Sales = 20 × Temperature + 200
Correct answer: Sales = 30 × Temperature − 100
From 10→15 (ΔT=5, ΔS=150, slope=30). Check: 30(10)−100=200 ✓, 30(15)−100=350 ✓, 30(20)−100=500 ✓. Equation A works.
Slope = (350 − 200)/(15 − 10) = 150/5 = 30. Using point (10, 200): 200 = 30(10) + b → b = 200 − 300 = −100. Equation: Sales = 30 × Temperature − 100. Verify with T=35: 30(35) − 100 = 1050 − 100 = 950 ✓.
Question 29: A comparative analysis shows two countries' GDP growth: Country A: 2018=$1T, 2023=$1.4T Country B: 2018=$500B, 2023=$800B Which country had a higher percentage GDP growth from 2018 to 2023? (A) Country A with 40% growth (B) Country B with 60% growth (C) Both had equal growth rates (D) Country A with 50% growth
- Country A with 40% growth
- Country B with 60% growth (Correct answer)
- Both had equal growth rates
- Country A with 50% growth
Correct answer: Country B with 60% growth
Country A: (1.4−1)/1 = 40%. Country B: (800−500)/500 = 60%. Country B had higher percentage growth.
Country A: ($1.4T − $1T) / $1T = $0.4T / $1T = 40% growth. Country B: ($800B − $500B) / $500B = $300B / $500B = 60% growth. Although Country A added $400B in absolute terms vs. Country B's $300B, Country B's smaller base means its percentage growth (60%) was higher.
Question 30: A normal distribution has mean = 100 and standard deviation = 15. Approximately what percentage of values fall between 85 and 115? (A) 34% (B) 50% (C) 68% (D) 95%
- 34%
- 50%
- 68% (Correct answer)
- 95%
Correct answer: 68%
85 and 115 are one standard deviation below and above the mean (100 ± 15). By the empirical rule, ~68% of data falls within ±1 SD.
85 = 100 − 15 = mean − 1σ. 115 = 100 + 15 = mean + 1σ. By the empirical rule (68-95-99.7 rule), approximately 68% of data in a normal distribution falls within one standard deviation of the mean.
Question 31: A graph shows that a town's population, which was 50,000 in 2010, grows at 3% per year. A second town starts with 80,000 people but shrinks at 2% per year. In approximately how many years will the first town surpass the second? (A) 8 years (B) 10 years (C) 12 years (D) 15 years
- 8 years
- 10 years
- 12 years
- 15 years (Correct answer)
Correct answer: 15 years
Town 1: 50000×1.03^t. Town 2: 80000×0.98^t. Set equal: 1.03^t/0.98^t = 80000/50000 = 1.6. (1.03/0.98)^t = (1.0510)^t = 1.6. t = ln(1.6)/ln(1.051) ≈ 0.470/0.0497 ≈ 9.5 ≈ 10 years.
50,000 × 1.03^t = 80,000 × 0.98^t. Dividing: (1.03/0.98)^t = 80,000/50,000 = 1.6. 1.03/0.98 ≈ 1.0510. So 1.051^t = 1.6. Taking logarithms: t × ln(1.051) = ln(1.6). t = ln(1.6)/ln(1.051) ≈ 0.4700/0.0497 ≈ 9.5 years, so about 10 years. (B) is correct.
Question 32: A survey of 500 employees found the following job satisfaction ratings (scale 1–5): Rating 1: 20 employees Rating 2: 60 employees Rating 3: 150 employees Rating 4: 200 employees Rating 5: 70 employees What is the weighted mean satisfaction rating? (A) 3.4 (B) 3.5 (C) 3.6 (D) 3.7
- 3.4 (Correct answer)
- 3.5
- 3.6
- 3.7
Correct answer: 3.4
Mean = (1×20 + 2×60 + 3×150 + 4×200 + 5×70)/500 = (20+120+450+800+350)/500 = 1740/500 = 3.48 ≈ 3.5.
Sum of (rating × frequency): 1×20=20, 2×60=120, 3×150=450, 4×200=800, 5×70=350. Total = 20+120+450+800+350 = 1,740. Mean = 1,740 ÷ 500 = 3.48. This is closest to 3.5, so (B) is correct.
Question 33: A graph shows a company's monthly user growth (in thousands) following a pattern: Month 1=2, Month 2=6, Month 3=18, Month 4=54. If this pattern continues, how many users (in thousands) does the company have in Month 6? (A) 162 (B) 486 (C) 1,458 (D) 4,374
- 162
- 486 (Correct answer)
- 1,458
- 4,374
Correct answer: 486
Pattern: each month multiplies by 3. Month 5: 54×3=162. Month 6: 162×3=486.
2 → 6 (×3), 6 → 18 (×3), 18 → 54 (×3). Common ratio = 3. Month 5: 54 × 3 = 162. Month 6: 162 × 3 = 486 thousand users.
A company's annual revenue (in millions) over five years was: Year 1: $120M, Year 2: $144M, Year 3: $172.8M, Year 4: $207.4M, Year 5: $248.8M.
What was the approximate average percentage growth rate per year?
(A) 15%
(B) 18%
(C) 20%
(D) 22%