book Maths Puzzle Numerical Ability

A movie theater sells adult tickets at $5.50 a ticket and $3.50 for a childs ticket. How many of each ticket was sold if 21 tickets were bought for $83.50

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Question
In large data sets(1,000 or more values),the mean is always one of the data values. Why would this be true or false?
Please explain and factor the polynomial:
n^2/4 - 9/16