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04 Aug 2025, 10:11
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Groups of 7: 4
Remaining students: 6
At a summer camp, a class of students participates in three different sessions: math, biology, and history.
• For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.
• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
• For the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each.
Select for Groups of 7 the number of groups that have 7 students each in the history session, and select for Remaining students the number of students in the remaining history group, that would be jointly consistent with the given information. Make only two selections, one in each column.
• For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.
• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
• For the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each.
Select for Groups of 7 the number of groups that have 7 students each in the history session, and select for Remaining students the number of students in the remaining history group, that would be jointly consistent with the given information. Make only two selections, one in each column.
| Groups of 7 | Remaining students | |
| 2 | ||
| 4 | ||
| 6 | ||
| 8 | ||
| 10 |
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Official Answer
Groups of 7: 4
Remaining students: 6
04 Aug 2025, 10:11
Kudos
Bookmarks
Official Solution:
The math session setup tells us that the students are divided so that one group has 4 students and all other groups have 5 students each. This means the total number of students is 4 more than a multiple of 5.
Similarly, in the biology session, one group has 4 students and all other groups have 6 students each. So, the total number of students is also 4 more than a multiple of 6.
Therefore, the number of students must be 4 more than a multiple of 30 (the LCM of 5 and 6), that is, 34, 64, 94, and so on.
In the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each. So, the total number of students must equal:
7 * (number of groups of 7) + (remaining students)
We now test the given options to see which combination gives a total equal to 34, 64, 94, etc.
Only the combination:
• Number of groups of 7 = 4
• Remaining students = 6
gives a total of 7 * 4 + 6 = 28 + 6 = 34, which satisfies the condition.
Correct answer:
Groups of 7 "4"
Remaining students "6"
Bunuel
The math session setup tells us that the students are divided so that one group has 4 students and all other groups have 5 students each. This means the total number of students is 4 more than a multiple of 5.
Similarly, in the biology session, one group has 4 students and all other groups have 6 students each. So, the total number of students is also 4 more than a multiple of 6.
Therefore, the number of students must be 4 more than a multiple of 30 (the LCM of 5 and 6), that is, 34, 64, 94, and so on.
In the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each. So, the total number of students must equal:
7 * (number of groups of 7) + (remaining students)
We now test the given options to see which combination gives a total equal to 34, 64, 94, etc.
Only the combination:
• Number of groups of 7 = 4
• Remaining students = 6
gives a total of 7 * 4 + 6 = 28 + 6 = 34, which satisfies the condition.
Correct answer:
Groups of 7 "4"
Remaining students "6"
