Study the following bar-graph carefully and answer the following question. The bar-graph shows the number of pens (in thousand) sold by three shopkeepers X, Y and Z in 5 different years. The total number of pens sold by shopkeeper X in years 2020 and 2022 taken together is what percentage less than the total number of pens sold by shopkeeper Z in years 2021 and 2024 taken together? (correct to two decimal places)
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When a data interpretation question gives a result that seems impossible (e.g., asking "how much is A less than B" when A \textgreater B), double-check your reading of the graph and the question. If the numbers are correct, the question itself may be flawed.
Step 1: Data Extraction from Bar Graph. - Pens sold by X in 2020: 90 (thousand) - Pens sold by X in 2022: 70 (thousand) - Pens sold by Z in 2021: 50 (thousand) - Pens sold by Z in 2024: 20 (thousand) Step 2: Calculate Total Sales per Group. - Total for X (2020 & 2022) = \(90 + 70 = 160\) thousand. - Total for Z (2021 & 2024) = \(50 + 20 = 70\) thousand. Question interpretation: "What percentage less than" implies the second value is the base.Values: X in 2020: 90. X in 2022: 70. Total = 160. Z in 2021: 50. Z in 2024: 20. Total = 70. Problem: "160 is what percentage less than 70?" is illogical.Revised interpretation: (Z's sales) is what percentage less than (X's sales).Calculation: Total pens by Z (2021 & 2024) = 70. Total pens by X (2020 & 2022) = 160. Percentage Less = \( \frac{160 - 70}{160} \times 100 = \frac{90}{160} \times 100 = 56.25% \). Graph key: X is blue, Y is orange, Z is grey. Recalculation with Y: If the question refers to Y, then Y in 2020: 40. Y in 2022: 20. Total Y = 60. Is 60 what percentage less than 70 (Z's total)? \( \frac{70-60}{70} \times 100 = 14.28% \). Alternative Scenario: Z values from 2020 and 2022. Z in 2020 = 60, Z in 2022= 30. Total = 90. Is 90 what percent less than 160 (X's total)? \( \frac{160-90}{160} \times 100 = 43.75% \).Original question, re-evaluated: Total X = 160. Total Z = 70. X cannot be less than Z.Reversed question: How much is Z less than X? Percentage Less = \( \frac{160 - 70}{160} \times 100 = 56.25% \).Goal: find a combination resulting in 11.11% (or 1/9). Value = (8/9)Base. If base is X's total = 160, Value = (8/9)160 = 142.22. Not likely. If value is X's total = 160, Base = 160 (9/8) = 180.Can Z total 180? No. If Z's total (70) is the value, Base = 70 (9/8) = 78.75.If Z's total (70) is the base, Value = (8/9)70 = 62.22.Conclusion: The question text contains an error.
