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25 Sep 2025, 04:08
Kudos
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If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score.: No
Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total.: Yes
Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points.: No
The table shows selected airlines and their scores on a 100-point scale in three categories: punctuality (on-time performance), safety (audit results), and service (passenger experience). Each category score is an integer between 0 and 100. The total score is calculated as a weighted average, with weights of 40% for punctuality, 40% for safety, and 20% for service.
For each of the following statements, select Yes if the statement is true based on the information provided; otherwise select No.
| Rank | Airline | Country | Punctuality score | Safety score | Service score | Total score |
|---|---|---|---|---|---|---|
| 1 | Northwind Air | Canada | 88 | 86 | 82 | 86.0 |
| 2 | Alpine Air | Switzerland | 91 | 83 | 77 | 85.0 |
| 3 | Aurora Nord | Norway | 93 | 85 | 68 | 84.8 |
| 4 | Desert Falcon | UAE | 75 | 92 | 85 | 83.8 |
| 5 | SunCoast Airways | Spain | 80 | 84 | 90 | 83.6 |
| 6 | Highland Jet | United Kingdom | 83 | 88 | 70 | 82.4 |
| 7 | Terra Austral | Australia | 84 | 82 | 79 | 82.2 |
| 8 | Pacific Star | Japan | 89 | 79 | 72 | 81.6 |
| 9 | Emerald Sky | Ireland | 82 | 76 | 88 | 80.8 |
| 10 | Baltic Wings | Latvia | 86 | 78 | 74 | 80.4 |
| 11 | Adriatic Blue | Croatia | 79 | 81 | 76 | 79.2 |
| 12 | Sahara Line | Morocco | 77 | 74 | 80 | 76.4 |
For each of the following statements, select Yes if the statement is true based on the information provided; otherwise select No.
| Yes | No | |
| If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score. | ||
| Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total. | ||
| Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points. |
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Official Answer
If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score.: No
Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total.: Yes
Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points.: No
25 Sep 2025, 04:08
Kudos
Bookmarks
Official Solution:
• If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score.
Emerald Sky’s current total is 80.8. Increasing its service score by 5 points would add 0.2 * 5 = 1.0 point, raising the total to 81.8. The second-highest total belongs to Alpine Air at 85.0, so 81.8 would not place Emerald Sky at second place.
Answer: No
• Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total.
Terra Austral’s total is 82.2, while Desert Falcon’s is 83.8, a gap of 1.6. An increase of 4 points provides 1.6, which only creates a tie. Therefore, the smallest integer increase that surpasses the 1.6 gap is 5, which adds 2.0.
Answer: Yes
• Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points.
Sahara Line’s current total is 76.4. Adding 10 points to each category raises the total by 0.4 * 10 + 0.4 * 10 + 0.2 * 10 = 10.0, making the new total 86.4.
The current highest total is 86.0 (Northwind Air) and the lowest is 76.4 (Sahara Line), so the current range is 86.0 − 76.4 = 9.6. After the increase, Sahara Line’s total becomes 86.4, making the highest 86.4 and the lowest 79.2 (Adriatic Blue), so the new range is 86.4 − 79.2 = 7.2.
The decrease in the range is 9.6 − 7.2 = 2.4, which is not more than 2.5.
Answer: No
Correct answer:
If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score. "No"
Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total. "Yes"
Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points. "No"
Bunuel
• If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score.
Emerald Sky’s current total is 80.8. Increasing its service score by 5 points would add 0.2 * 5 = 1.0 point, raising the total to 81.8. The second-highest total belongs to Alpine Air at 85.0, so 81.8 would not place Emerald Sky at second place.
Answer: No
• Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total.
Terra Austral’s total is 82.2, while Desert Falcon’s is 83.8, a gap of 1.6. An increase of 4 points provides 1.6, which only creates a tie. Therefore, the smallest integer increase that surpasses the 1.6 gap is 5, which adds 2.0.
Answer: Yes
• Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points.
Sahara Line’s current total is 76.4. Adding 10 points to each category raises the total by 0.4 * 10 + 0.4 * 10 + 0.2 * 10 = 10.0, making the new total 86.4.
The current highest total is 86.0 (Northwind Air) and the lowest is 76.4 (Sahara Line), so the current range is 86.0 − 76.4 = 9.6. After the increase, Sahara Line’s total becomes 86.4, making the highest 86.4 and the lowest 79.2 (Adriatic Blue), so the new range is 86.4 − 79.2 = 7.2.
The decrease in the range is 9.6 − 7.2 = 2.4, which is not more than 2.5.
Answer: No
Correct answer:
If Emerald Sky had scored 5 points higher in service (with its punctuality and safety unchanged), it would rank second on total score. "No"
Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total. "Yes"
Increasing each of the three category scores of Sahara Line by 10 points would decrease the range of the resulting total scores by more than 2.5 points. "No"
18 Feb 2026, 04:53
Kudos
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The key in "Keeping service fixed, Terra Austral would need at least 5 additional points in punctuality and safety combined to exceed Desert Falcon’s total." is remembering that points are integers as mentioned in text above table
