Question 19. There are 60 students on a trip. When they line up, the colors of their reflective vests follow the pattern yellow-green-yellow-green. The colors of their backpacks follow a different pattern, red-brown-orange-red-brown-orange. How many students with a yellow reflective vest also have an orange backpack? Let's start off by writing an example of the first 15 students. We know that their vests are yellow-green-yellow-green, and so on, so we will draw that out. Now we know that their backpacks are red-brown-orange. We are representing their colors by letters. Now we are being asked how many students have yellow vests and orange backpacks. So I will highlight those students. The 3rd student, 9th student, and 15th student. With this, we see a pattern. Starting with the 3rd student, if we add 6, each student will have this combination. So student 3, student 9, student 15, student 21, student 27, 33, 39, 45, 51, and 57. We stop here because the next student in this pattern would be 63, but there's only 60 students on this strip. So we add up how many different students we have here, and get our answer, which is E, 10.

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