16. There are more than 20 and fewer than 30 children in Miss Tree's class. They are all standing in a circle. Anna notices that there are six times as many children between her and Zara going round the circle clockwise, as there are going round anti-clockwise. How many children are there in the class?
A 23
B 24
C 25
D 26
E 27
Solution
A

Let the number of children between Anna and Zara going round the circle anti-clockwise be $n$. Therefore, there are $6 n$ children between Anna and Zara going round the circle clockwise. Hence, including Anna and Zara, there are $7 n+2$ children in the circle. The only number more than 20 and less than 30 that is of the form $7 n+2$ is 23 . Therefore there are 23 children in Miss Tree's class.