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A certain marching band has fewer than 50 members. During performances
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16 Nov 2023, 03:42
16 Nov 2023, 03:42
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A certain marching band has fewer than 50 members. During performances, the members march in different formations. When they march in Formation A, each row has 5 members, except the last row, which has 3 members. When they march in Formation B, each row has 6 members, except the last row, which has 5 members. If they march in Formation C, each row has 7 members, except the last row. How many band members are in the last row in Formation C?
A) 1
B) 2
C) 3
D) 4
E) 6
A) 1
B) 2
C) 3
D) 4
E) 6
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Re: A certain marching band has fewer than 50 members. During performances
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16 Nov 2023, 06:13
16 Nov 2023, 06:13
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hugogva wrote:
A certain marching band has fewer than 50 members. During performances, the members march in different formations. When they march in Formation A, each row has 5 members, except the last row, which has 3 members. When they march in Formation B, each row has 6 members, except the last row, which has 5 members. If they march in Formation C, each row has 7 members, except the last row. How many band members are in the last row in Formation C?
A) 1
B) 2
C) 3
D) 4
E) 6
A) 1
B) 2
C) 3
D) 4
E) 6
Let the number of members in the band = n
When they march in Formation A, each row has 5 members, except the last row, which has 3 members.
\(n = 5x_1 + 3\)
\(x_1\) → Number of rows that have 5 members
When they march in Formation B, each row has 6 members, except the last row, which has 5 members.
\(n = 6x_2 + 5\)
\(x_2\) → Number of rows that have 6 members
Combining both of the information, we can combine
\(n = \text{LCM}(6,5)x + \text{first common term}\)
\(n = 5x_1 + 3\) ⇒ 3, 8, 13, 18, 23, ....
\(n = 6x_2 + 5\) ⇒ 5, 11, 17, 23, ....
Therefore
\(n = \text{LCM}(6,5)x + 23\)
As the number of members is fewer than 50, the number of members in the marching band = 23
Question: If they march in Formation C, each row has 7 members, except the last row. How many band members are in the last row in Formation C?
Inference: The question requires us to find the remainder when the number of members in the marching band, i.e. 23, is divisible by 7.
\(23 = 7 * 3 + 2\)
Remainder = \(2\)
Option B
General Discussion
Re: A certain marching band has fewer than 50 members. During performances
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25 Dec 2023, 19:47
25 Dec 2023, 19:47
Sorry, but this is a problem I just do not understand. How could we be sure the lowest combo of the two formulas would be the correct one that seven would also be apart of? Why is there an LCM if we don't use it?
