Question

If the median of seven consecutive prime numbers is 67, then the difference between the highest and the lowest number is

• A. 13
• B. 26
• C. 20
• D. 12

Answer 1

The correct option is B 26

Given that the median of 7 consecutive prime numbers is 67.
$\therefore n=7$
$\Rightarrow$ Median of 7 observations = $(\frac{n+1}{2}{)}^{th}$ term
= $4^{th}$ term
Thus, the 4th term is 67. This means that there are 3 terms to the left and 3 terms to the right of 67 and all of them are prime numbers.
Therefore, the 7 consecutive prime numbers are 53, 59, 61, 67, 71, 73, 79.
$\therefore$ Difference of highest and lowest prime numbers = 79 – 53 = 26
Hence, the correct answer is option (b).