The average of five different positive numbers

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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
**

## Show Answer

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Answer-A
Solution-

__Solution(By Apex 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
$\Large\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}}{5}=25$
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 < e < 25
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
$25>\Large\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+0}{5} \Rightarrow 20$ 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

The average of five different positive numbers