Number System
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Q.

A set has exactly five consecutive positive integers starting with 1.

What is the percentage decrease in the average of the numbers when the greatest one of the numbers is removed from the set?

 A.

8.54

 B.

12.56

 C.

15.25

 D.

16.66

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Solution:
Option(D) is correct

The average of the five consecutive positive integers $1, 2, 3, 4$ and $5$ is:
$\dfrac{(1 + 2 + 3 + 4 + 5)}{5} = \dfrac{15}{5} =3$

After dropping 5 (the greatest number), the new average becomes:
$\dfrac{(1 + 2 + 3 + 4)}{4} = \dfrac{10}{4} = 2.5.$

\begin{align*}
\text{% drop in the average}&=\\
&= \dfrac{\text{Old average – New average}}{\text{Old average}}× 100\\
\Rightarrow \dfrac{3− 2.5}{3} × 100 &=\dfrac{100}{6} \\
&= 16.66%
\end{align*}


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