Question

The range of numbers $x_1,x_2,x_3,x_4,x_5$ is $r$ where $x_i<x_{i+1}$. If each number is multiplied by $p(p>0)$ and then $k$ is subtracted from each number, then the range of new numbers is

• A. $pr$
• B. $pr-k$
• C. $p$
• D. $p(r-k)$

Answer 1

The correct option is A $pr$

Range of $x_1,x_2,x_3,x_4,x_5$ is $x_5-x_1=r$

Now, for new data
$x_i^{\prime }=p{x}_i-k$
Range
$=x_5^{\prime }-x_1^{\prime }=p{x}_5-k-(p{x}_1-k)=p(x_5-x_1)=pr$