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### The average of five different positive numbers is 25. x is the decrease in the average when the smallest number among them is replaced by 0. What can be said about x?

- A. x is less than 5
- B. x is greater than 5
- C. x is equal to 5
- D. Cannot be determined

**Answer: Option A **

Here is complete explanation of The average of five different positive numbers is 25 x is….

__Solution(By ExamCraze Team)__

Let a, b, c, d, and e be the five positive numbers in the decreasing order of size such that e is the smallest number.

We are given that the average of the five numbers is 25. Hence, we have the equation
$$frac{{{text{a}} + {text{b}} + {text{c}} + {text{d}} + {text{e}}}}{5} = 25$$

a + b + c + d + e = 125 ----------- (1) by multiplying by 5.
The smallest number in a set is at least less than the average of the numbers in the set if at least one number is different.
For example, the average of 1, 2, and 3 is 2, and the smallest number in the set 1 is less than the
average 2. Hence, we have the inequality
0
0 > -e > -25 by multiplying both sides of the inequality by -1 and flipping the directions of the inequalities.
Adding this inequality to equation (1) yields
0 + 125 > (a + b + c + d + e) + (-e) > 125 - 25
125 > (a + b + c + d) > 100
125 > (a + b + c + d + 0) > 100 by adding by 0
25 > $$frac{{{text{a}} + {text{b}} + {text{c}} + {text{d}} + 0}}{5}$$ ⇒ 20 by dividing the inequality by 5

25 > The average of numbers a, b, c, d and 0 > 20

Hence, x equals

(Average of the numbers a, b, c, d and e) – (Average of the numbers a, b, c, and d)

= 25 − (A number between 20 and 25)

⇒ A number less than 5

Hence, x is less than 5