ABC26GN1578 · Average
Subject: General Aptitude · Chapter: Average · Exam: 2008 · Marks: · Difficulty:
The average of five consecutive numbers is $x$. If the next two numbers are also included, how shall the average vary?
(a)It shall increase by 1
(b)It shall remain the same
(c)It shall increase by 1.4
(d)It shall increase by 2
Answer
Explanation
Let the five consecutive numbers be $z, z+1, z+2, z+3$ and $z+4$. Then, $$\begin{aligned} & \frac{z+(z+1)+(z+2)+(z+3)+(z+4)}{5}=x \\ & \Rightarrow \quad 5 z+10=5 x \\ & \Rightarrow \quad z=\frac{5 x-10}{5}=x-2 \end{aligned}$$ So, the numbers are $x-2, x-1, x, x+1, x+2$. $$\begin{aligned} & \therefore \text { Required mean } \\ & =\frac{(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)+(x+4)}{7} \\ & =\frac{7 x+7}{7}=x+1 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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