You are an AI assistant that helps people find information. User will you give you a question. Your task is to answer as faithfully as you can. While answering think step-by-step and justify your answer.
system
People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a white shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?
Options:
(A) 29
(B) 39
(C) 54
(D) 64
(E) 75 Stream of consciousness first, then make a decision:
user
To figure out which of the following options cannot be the number of people in the line, we can analyze the pattern and apply it to each option.

The pattern is red, green, blue, white, and yellow (5 colors), and it ends with a white shirt. Let's assign a number to each color in the pattern:
1 - red
2 - green
3 - blue
4 - white
5 - yellow

Since the pattern ends with a white shirt, we know that the number of people in the line will be a multiple of 5, plus 3 (to account for the blue, white, and yellow shirts). In other words, the number of people in the line must be in the form 5n + 3.

Now let's apply this rule to the given options:

(A) 29
Is 29 in the form 5n + 3?
29 - 3 = 26
26 / 5 = 5 with a remainder of 1.
No, 29 is not in the form 5n + 3.

(B) 39
Is 39 in the form 5n + 3?
39 - 3 = 36
36 / 5 = 7 with a remainder of 1.
No, 39 is not in the form 5n + 3.

(C) 54
Is 54 in the form 5n + 3?
54 - 3 = 51
51 / 5 = 10 with a remainder of 1.
No, 54 is not in the form 5n + 3.

(D) 64
Is 64 in the form 5n + 3?
64 - 3 = 61
61 / 5 = 12 with a remainder of 1.
No, 64 is not in the form 5n + 3.

(E) 75
Is 75 in the form 5n + 3?
75 - 3 = 72
72 / 5 = 14 with a remainder of 2.
No, 75 is not in the form 5n + 3.

Since none of the options fit the 5n + 3 pattern, we can conclude that none of these options can be the number of people in the line.
assistant