The average of five consecutive odd numbers is 95. What is the fourth number in the descending order?

### Concept & Logic The average of any set of consecutive odd or even numbers (which form an Arithmetic Progression) is always its median. If the number of terms is odd, the average is the exact middle term. ### Step-by-Step Solution * **Given:** * There are $5$ consecutive odd numbers. * Their average is $95$. * **Deduction:** * Since $5$ is an odd number of terms, the 3rd term (the middle one) must be the average, $95$. * Consecutive odd numbers differ by $2$. * **Calculation:** * The numbers in ascending order are: $91, 93, 95, 97, 99$. * The question asks for the sequence in **descending order**. Let's reverse it: * $99, 97, 95, 93, 91$. * The fourth number in this descending sequence is $93$. * Checking the options: (a) 91, (b) 95, (c) 97, (d) 99. * $93$ is not listed. ### Exam Strategy & Shortcut Identify the middle term ($95$). Write the set out quickly: $\{91, 93, 95, 97, 99\}$. Descending means starting from the largest. $99$ (1st), $97$ (2nd), $95$ (3rd), $93$ (4th). Look at options, pick "None of these". ### Common Pitfall Ignoring the word "descending". If you simply look for the 4th number in the standard (ascending) order, you will find $97$, which is Option (c). Examiners specifically include this to catch students who read the question too quickly. ### Final Answer **Therefore, the correct answer is None of these.**