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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 $x$?


$x$ is less than 5


$x$ is greater than 5


$x$ is equal to 5


Nothing can be said

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Option(A) is correct

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



$a+b+c+d+e=125$----------- (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

$0>–e>–25$ by multiplying both sides of the inequality by –1 and flipping the directions of

the inequalities.

Adding this inequality to equation (1) yields



$125>(a+b+c+d+0)>100$ by adding by 0

\(25>\dfrac{a+b+c+d+0}{5}=>20\)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.

(3) Comment(s)


Really nice one Cool


If we remove a number less than the average the average should increase and not decrease.

In the above question the average decreases by $x$ does it mean $x$ is negative. Huh


but that is if the number of quantities also decrease but in this case , number of quantities remain same and one quantity is put equal to zero hence the average is decreasing... Smile