Question 995343: The average of 4 positive numbers is 8. If all the numbers are less than 10, none of these numbers could be...
A. 2
B. 3.5
C. 8
D. 9.9
Answer by ikleyn(52908)   (Show Source):
You can put this solution on YOUR website! .
The average of 4 positive numbers is 8. If all the numbers are less than 10, none of these numbers could be...
A. 2
B. 3.5
C. 8
D. 9.9
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Answer. . . . None of these numbers could be 2.
Solution
Let these four numbers be a, b, c and d.
Since the average (I mean, arithmetic average) of 4 positive numbers is 8, their sum is 4*8 = 32.
If some of the numbers, let say, a, is 2, then
a + b + c + d = 2 + (b + c + d) < 32,
since (b + c + d) is less than 3*10 = 30, according to the condition.
Thus from one side,
a + b + c + d = 32.
From the other side
a + b + c + d < 32.
Contradiction.
This proof works for "2" and does not work for other numbers of the cases B, C and D.
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