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08 Jul 2025, 19:18
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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.
4 + 5x
• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
4 + 6y
• 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.
(s<7) + 7z
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 for first two conditions, we need numbers that will leave remainder 4 when divided by 5 or 6;
5*6 = 30; Multiple of 30 + 4; so those no. can be 34,64,94.......;
Options for 7’s Group and Remainder are 2,4,6,8,10;
Now remainder must be lower than 7, so can be 2,4,6;
34: 7 * 4 + 6; Matching the options; 4 group and 6 as remainder. Answer.
• For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.
4 + 5x
• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
4 + 6y
• 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.
(s<7) + 7z
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 for first two conditions, we need numbers that will leave remainder 4 when divided by 5 or 6;
5*6 = 30; Multiple of 30 + 4; so those no. can be 34,64,94.......;
Options for 7’s Group and Remainder are 2,4,6,8,10;
Now remainder must be lower than 7, so can be 2,4,6;
34: 7 * 4 + 6; Matching the options; 4 group and 6 as remainder. Answer.
08 Jul 2025, 19:33
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We have T is the total students participate at a summer camp.
For math session, T= 4 + 5*M ( M is the number of the group of five) (1)
For biology session, T= 4 + 6*B ( B is the number of the group of six) (2)
For history session, T= <7 + 7*H ( H is the number of the group of seven) (3)
From (1) (2) we have T should have LCM (5,6), which mean T = 4 +30*B (B could be 1,2,....)
Based on the answer and (3), T could be 34 then H (Groups of 7) = 4, Remaining students will ve 34-7*4=6
For math session, T= 4 + 5*M ( M is the number of the group of five) (1)
For biology session, T= 4 + 6*B ( B is the number of the group of six) (2)
For history session, T= <7 + 7*H ( H is the number of the group of seven) (3)
From (1) (2) we have T should have LCM (5,6), which mean T = 4 +30*B (B could be 1,2,....)
Based on the answer and (3), T could be 34 then H (Groups of 7) = 4, Remaining students will ve 34-7*4=6
Bunuel
08 Jul 2025, 20:17
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As per the division of students in Math and Biology sessions, it's clear that groups of 5 and groups of 6 should have a common point. Taking LCM we find it's 30.
This means there are a total of 30 + 4 = 34 students.
For Groups of 7, the answer is 4 (7 x 4 = 28) and remaining students will be (34-28=) 6.
This means there are a total of 30 + 4 = 34 students.
For Groups of 7, the answer is 4 (7 x 4 = 28) and remaining students will be (34-28=) 6.
Bunuel
