A number of children are standing in a circle. They are evenly spaced and the 5th child is directly opposite the 18th child. How many children are there altogether?
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14
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28
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32
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64
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20
If the 5th child is directly opposite the 18th child, there must be 13 children between them going one way around the circle (positions 6 through 18). Since they're opposite each other, there must also be 13 children going the other way, meaning 13 children separate them in both directions. With 13 children between them and the two end children themselves, we get 13 × 2 + 2 = 28 children total. In a circle of 28, position 5 is opposite position 19 (5 + 14 = 19), which is child 18 when counting from 5.
To solve this problem, we can use the concept of divisibility and remainders.
Let's assume that there are "n" children standing in the circle.
Since the 5th child is directly opposite the 18th child, we can say that the distance between them is half of the total number of children minus 1.
So, the distance between the 5th and 18th child is (n/2 - 1).
Since they are evenly spaced, we can also say that the distance between the 5th and 18th child is (18 - 5) = 13.
Therefore, we have the equation: (n/2 - 1) = 13.
Now, let's solve for "n":
n/2 - 1 = 13 n/2 = 14 n = 28
Therefore, there are 28 children altogether.
The correct answer is B) 28.