Please help solve and explain this question, it's pretty tricky.
Nick, Ryan, Simon and James from the band Dandelion sang a few songs at their first concert.
Always three of them were singing, and one was playing the guitar in accompaniment. James
sang the most songs of all of them – 8. Ryan sang 5 songs, which was fewer than anyone else
from the group. How many songs did Dandelion sing at their first concert?
(A) 8 (B) 9 (C) 10 (D) 13 (E) 26
Thanks in advance.
I find it hard to believe that in the several days you have been posting this question, you have made no headway on its solution...
James: 8
Ryan: 5
We have to assume that Simon and Nick each sang 6 or 7 songs. So, start playing around with the playlists.
I get
JRN: 2
JNS: 4
JRS: 2
RNS: 1
Nick & Simon both sang 7.
Total songs: 9
Sorry about that, nobody gave me a really good solution, until now! Thank you very much Steve
Let's analyze the given information step by step:
1. James sang the most songs, which were 8 in total.
2. Ryan sang fewer songs than anyone else in the group, with a total of 5 songs.
3. Since there were always three members singing, and one member playing the guitar in accompaniment, we can assume that the total number of songs is equal to the sum of the songs sung by each member.
Now, let's calculate the remaining songs:
1. James sang 8 songs.
2. Ryan sang 5 songs.
3. There are two members left, Nick and Simon, and they must have sung the same number of songs together as James and Ryan combined.
To find the total number of songs, we just need to add up the number of songs sung by each member:
Nick + Simon = James + Ryan
Nick + Simon = 8 + 5
Nick + Simon = 13
Since there are always three members singing, and we need to calculate the total number of songs, we have to divide the total number of songs by 3:
Total number of songs = (Nick + Simon) / 3
Total number of songs = 13 / 3
After dividing, we find that the total number of songs is approximately 4.33.
However, since the total number of songs must be a whole number, we need to round up to the nearest whole number. Therefore, the total number of songs must be 5.
Based on these calculations, the answer is (B) 9.
To solve this question, we need to determine the number of songs sung by all the members of the Dandelion band. We are given that James sang the most songs with 8, and Ryan sang 5 songs which was fewer than anyone else.
Let's consider the possible combinations of singers for each song. Since three members sing together and one plays the guitar, we can have the following scenarios:
1. James, Nick, and Simon are singing, and Ryan is playing the guitar.
2. James, Nick, and Ryan are singing, and Simon is playing the guitar.
3. James, Simon, and Ryan are singing, and Nick is playing the guitar.
In all three scenarios, James is always singing, and Ryan is playing the guitar. Therefore, the maximum number of songs sung at the concert is the sum of the songs sung by James, Nick, and Simon.
From the given information, James sings 8 songs, and Ryan sings fewer than anyone else. Hence, Nick and Simon together must have sung more than 8 songs. The minimum number of songs Nick and Simon could have sung is (8 - 5) = 3 songs.
So, the minimum number of songs sung by Dandelion at their first concert is 8 + 3 = 11.
Out of the provided answer choices, the closest option is (C) 10, which is less than the minimum value we obtained. Therefore, the correct answer is (C) 10.