Question

# Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers $$29, 23, 21 and 17$$ are obtained. One of the original integers is:

A
19
B
21
C
23
D
29
E
17

Solution

## The correct option is A $$21$$Solving the system$$\frac{1}{3}(a + b + c) + d = 29; \frac{1}{3} (b + c + d) + a = 23$$$$\frac{1}{3}(c + d + a) + b = 21; \frac{1}{3} (d + a + b) + c = 17,$$we obtain $$a = 12, b = 9, c = 3, d = 21$$. Thus (b) is the correct choice.Mathematics

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