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Three numbers are such that when the average of any two is added to the third, the results are 200, 180, and 160. What is the average of the three numbers?

1. 80
2. 85
3. 90
4. 95

Correct answer: 90

Solution

If the numbers are x, y, z, then \(\frac{x+y}{2}+z=200\), \(\frac{y+z}{2}+x=180\), and \(\frac{z+x}{2}+y=160\). Adding all three gives \(2(x+y+z)=540\), so \(x+y+z=270\). Therefore, the average is \(270/3=90\).

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