One-fourth of the sum of prime numbers, greater than 4 but less than 16, is the square of

### Concept & Strategy This is a multi-step arithmetic reasoning problem. It requires identifying prime numbers within a specific range, performing basic operations, and then finding the number whose square matches the result. Prime Number Definition: $$ \text{A number divisible only by 1 and itself.} $$ ### Step-by-Step Solution - **Step 1: Identify the prime numbers.** - We need prime numbers greater than $4$ and less than $16$. - These prime numbers are: $5, 7, 11, \text{ and } 13$. - **Step 2: Find their sum.** - Sum = $5 + 7 + 11 + 13 = 36$. - **Step 3: Calculate one-fourth of the sum.** - One-fourth of $36$ = $\frac{36}{4} = 9$. - **Step 4: Relate back to the question.** - The result is $9$. The question asks: "$9$ is the square of what number?" - Since $3^2 = 9$, the required number is $3$. ### Exam Strategy & Shortcut Write down the primes quickly: $5, 7, 11, 13$. Add them in pairs to be faster: $(13+7) + (11+5) = 20 + 16 = 36$. Divide by $4$ to get $9$. The square root of $9$ is $3$. This entire process should take less than 15 seconds. ### Common Pitfall Including numbers that are not prime, such as $9$ or $15$, in the initial list. Remember that $9$ is divisible by $3$, and $15$ is divisible by $3$ and $5$. Also, failing to read the final part of the prompt "is the square of" and looking for $9$ in the options. ### Final Answer Therefore, the correct answer is 3.