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

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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

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