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24 Sep 2025, 09:50
Kudos
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Exactly half of the teams shifted tiers between 2015 and 2025.: Yes
More than 5 teams improved their placement from 2015 to 2025.: No
The Tigers’ movement exceeded the median movement of all 12 teams.: No
A regional basketball league listed the final placements of 12 teams in both the 2015 and 2025 seasons. Placement 1 corresponds to the team with the best record that year. In addition to numerical placement, the league also classifies teams into tiers based on placement: Tier A (positions 1–4), Tier B (5–8), and Tier C (9–12).
Movement is defined as (2015 placement) − (2025 placement). A positive value means the team improved its placement, while a negative value means the team dropped in placement.
For each of the following statements concerning the teams in this sample, select Yes if the statement is supported by the information provided; otherwise, select No.
| Team | Placement 2015 | Placement 2025 |
|---|---|---|
| Falcons | 2 | 6 |
| Hawks | 5 | 3 |
| Tigers | 8 | 10 |
| Bulls | 12 | 9 |
| Eagles | 6 | 2 |
| Sharks | 9 | 11 |
| Wolves | 4 | 5 |
| Lions | 11 | 12 |
| Panthers | 1 | 4 |
| Raptors | 7 | 8 |
| Cobras | 10 | 7 |
| Bears | 3 | 1 |
Movement is defined as (2015 placement) − (2025 placement). A positive value means the team improved its placement, while a negative value means the team dropped in placement.
For each of the following statements concerning the teams in this sample, select Yes if the statement is supported by the information provided; otherwise, select No.
| Yes | No | |
| Exactly half of the teams shifted tiers between 2015 and 2025. | ||
| More than 5 teams improved their placement from 2015 to 2025. | ||
| The Tigers’ movement exceeded the median movement of all 12 teams. |
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Official Answer
Exactly half of the teams shifted tiers between 2015 and 2025.: Yes
More than 5 teams improved their placement from 2015 to 2025.: No
The Tigers’ movement exceeded the median movement of all 12 teams.: No
24 Sep 2025, 09:50
Kudos
Bookmarks
Official Solution:
• Exactly half of the teams shifted tiers between 2015 and 2025.
Tier A = 1–4, Tier B = 5–8, Tier C = 9–12.
Falcons went from 2 to 6, which is A to B, so shifted.
Hawks went from 5 to 3, which is B to A, so shifted.
Tigers went from 8 to 10, which is B to C, so shifted.
Bulls went from 12 to 9, which is C to C, so no shift.
Eagles went from 6 to 2, which is B to A, so shifted.
Sharks went from 9 to 11, which is C to C, so no shift.
Wolves went from 4 to 5, which is A to B, so shifted.
Lions went from 11 to 12, which is C to C, so no shift.
Panthers went from 1 to 4, which is A to A, so no shift.
Raptors went from 7 to 8, which is B to B, so no shift.
Cobras went from 10 to 7, which is C to B, so shifted.
Bears went from 3 to 1, which is A to A, so no shift.
In total, 6 of the 12 teams shifted tiers, which is exactly half.
Answer: Yes
• More than 5 teams improved their placement from 2015 to 2025.
Falcons: 2 − 6 = −4, decline.
Hawks: 5 − 3 = +2, improvement.
Tigers: 8 − 10 = −2, decline.
Bulls: 12 − 9 = +3, improvement.
Eagles: 6 − 2 = +4, improvement.
Sharks: 9 − 11 = −2, decline.
Wolves: 4 − 5 = −1, decline.
Lions: 11 − 12 = −1, decline.
Panthers: 1 − 4 = −3, decline.
Raptors: 7 − 8 = −1, decline.
Cobras: 10 − 7 = +3, improvement.
Bears: 3 − 1 = +2, improvement.
That gives 5 improvements in total: Hawks, Bulls, Eagles, Cobras, and Bears. Since 5 is not more than 5, the statement is not true.
Answer: No
• The Tigers’ movement exceeded the median movement of all 12 teams.
Tigers’ movement = 8 − 10 = −2.
Movements for all teams: Falcons −4, Hawks +2, Tigers −2, Bulls +3, Eagles +4, Sharks −2, Wolves −1, Lions −1, Panthers −3, Raptors −1, Cobras +3, Bears +2.
Ordered values: −4, −3, −2, −2, −1, −1, −1, +2, +2, +3, +3, +4.
With 12 teams, the median is the average of the 6th and 7th values. Both are −1, so the median movement is −1. Tigers’ movement is −2, which is less than −1, so it did not exceed the median.
Answer: No
Correct answer:
Exactly half of the teams shifted tiers between 2015 and 2025. "Yes"
More than 5 teams improved their placement from 2015 to 2025. "No"
The Tigers’ movement exceeded the median movement of all 12 teams. "No"
Bunuel
• Exactly half of the teams shifted tiers between 2015 and 2025.
Tier A = 1–4, Tier B = 5–8, Tier C = 9–12.
Falcons went from 2 to 6, which is A to B, so shifted.
Hawks went from 5 to 3, which is B to A, so shifted.
Tigers went from 8 to 10, which is B to C, so shifted.
Bulls went from 12 to 9, which is C to C, so no shift.
Eagles went from 6 to 2, which is B to A, so shifted.
Sharks went from 9 to 11, which is C to C, so no shift.
Wolves went from 4 to 5, which is A to B, so shifted.
Lions went from 11 to 12, which is C to C, so no shift.
Panthers went from 1 to 4, which is A to A, so no shift.
Raptors went from 7 to 8, which is B to B, so no shift.
Cobras went from 10 to 7, which is C to B, so shifted.
Bears went from 3 to 1, which is A to A, so no shift.
In total, 6 of the 12 teams shifted tiers, which is exactly half.
Answer: Yes
• More than 5 teams improved their placement from 2015 to 2025.
Falcons: 2 − 6 = −4, decline.
Hawks: 5 − 3 = +2, improvement.
Tigers: 8 − 10 = −2, decline.
Bulls: 12 − 9 = +3, improvement.
Eagles: 6 − 2 = +4, improvement.
Sharks: 9 − 11 = −2, decline.
Wolves: 4 − 5 = −1, decline.
Lions: 11 − 12 = −1, decline.
Panthers: 1 − 4 = −3, decline.
Raptors: 7 − 8 = −1, decline.
Cobras: 10 − 7 = +3, improvement.
Bears: 3 − 1 = +2, improvement.
That gives 5 improvements in total: Hawks, Bulls, Eagles, Cobras, and Bears. Since 5 is not more than 5, the statement is not true.
Answer: No
• The Tigers’ movement exceeded the median movement of all 12 teams.
Tigers’ movement = 8 − 10 = −2.
Movements for all teams: Falcons −4, Hawks +2, Tigers −2, Bulls +3, Eagles +4, Sharks −2, Wolves −1, Lions −1, Panthers −3, Raptors −1, Cobras +3, Bears +2.
Ordered values: −4, −3, −2, −2, −1, −1, −1, +2, +2, +3, +3, +4.
With 12 teams, the median is the average of the 6th and 7th values. Both are −1, so the median movement is −1. Tigers’ movement is −2, which is less than −1, so it did not exceed the median.
Answer: No
Correct answer:
Exactly half of the teams shifted tiers between 2015 and 2025. "Yes"
More than 5 teams improved their placement from 2015 to 2025. "No"
The Tigers’ movement exceeded the median movement of all 12 teams. "No"
23 Nov 2025, 02:15
Kudos
Bookmarks
how to solve these kind of questions in less than 3 minutes? where so much mechanical calculations are required
