##
**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

### 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
## Related Questions On Average

### Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average19 people went to a hotel for combine dinner party 13 by 8 runs. His new average is:

A. 20B. 21

C. 28

D. 32

### Find the average of all the numbers between 6 and 34 which are divisible by 5.

A. 18B. 20

C. 24

D. 30

### In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?

A. 10 yearsB. 10.5 years

C. 11 years

D. 12 years

### If the arithmetic mean of 0, 5, 4, 3 is a, that of -1, 0, 1, 5, 4, 3 is b and that of 5, 4, 3 is c, then the relation between a, b, and c is.

A. a = b = cB. a : b : c = 3 : 2 : 4

C. 4a = 5b = c

D. a + b + c = 12