Question

All the batsmen in the Orange county cricket team, have an average run per test match between 155 and 273. Which of the following inequalities can be used to determine whether a batsman with an average run per test match, r, could be in the team?

• A. $|r+155|<273$
• B. $|r-273|<59$
• C. $|r-214|<59$
• D. $|r+273|<155$

Answer 1

The correct option is C $|r-214|<59$

Given, r is the average run per test match.
According to, the question, the average run of a batsman on the team is given by the inequality
$155<r<273$

Step 1 : Calculate the mid value
The mid value of {155, 273} is $\frac{(155+273)}{2}=214$

Step 2 : Calculate the distance of the mid value from the range
214 - 155 = 59 [You can use either of the range value!]
Thus, the inequality is
$|r-214|<59$
Hence, option C is correct.