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12 Nov 2024, 03:49
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Minimum: 15
Impossible: 25
A group of friends plans to travel to a neighboring island for their summer vacation but is divided on the mode of transport. Exactly two-fifths of the group wants to travel by ship, while exactly one-third prefers air travel.
In the table below, select for Minimum the least possible number of friends in the group, and select for Impossible the option that cannot be the number of friends in the group. Make only two selections, one in each column.
In the table below, select for Minimum the least possible number of friends in the group, and select for Impossible the option that cannot be the number of friends in the group. Make only two selections, one in each column.
| Minimum | Impossible | |
| 15 | ||
| 25 | ||
| 30 | ||
| 45 | ||
| 75 | ||
| 105 |
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Official Answer
Minimum: 15
Impossible: 25
12 Nov 2024, 03:49
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Official Solution:
Since exactly 2/5 of the group wants to travel by ship and exactly 1/3 prefers air travel, the total number of friends must be a multiple of 3 * 5 = 15. This makes the least possible number of friends in the group 15, and any option that is not a multiple of 15 impossible. Among the options, only 25 is not a multiple of 15.
Correct answer:
Minimum "15"
Impossible "25"
Bunuel
Since exactly 2/5 of the group wants to travel by ship and exactly 1/3 prefers air travel, the total number of friends must be a multiple of 3 * 5 = 15. This makes the least possible number of friends in the group 15, and any option that is not a multiple of 15 impossible. Among the options, only 25 is not a multiple of 15.
Correct answer:
Minimum "15"
Impossible "25"
03 Feb 2025, 09:38
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
