Select the correct answer 121 : 12 : : 25 : ? radio_button_unchecked 1 radio_button_unchecked 3 radio_button_unchecked 6 radio_button_unchecked 7

Break Down the Problem

1. We need to identify the relationship between the numbers in the ratio $121 : 12$ and then apply that relationship to the numbers $25 : ?$.

Relevant Concepts

2. The first part of the ratio is $121$ and the second part is $12$. To find the missing part of the ratio corresponding to $25$, we need to establish a mathematical operation that transforms $121$ into $12$.

Analysis and Detail

3. Let's analyze $121$ and $12$:
   • The number $121$ can be expressed as $11^2$.
   • The number $12$ can be derived as follows: $12 = 121 \div 10.0833 \text{ approximately (or } 121 : 10 \text{ )}$

Next, apply this to $25$:

• We use the same divisor to find $? = 25 \div k$ where $k \approx 10.0833$:
• Therefore, $? = 25 \div 10.0833 \approx 2.48$.

Now let's see which option fits closely to this result:

• None of the options appear to match exactly to $2.48$, but rounding may make a difference.

Verify and Summarize

4. Checking the closest integer values for simplicity, the options provided are $1, 3, 6, 7$. The closest integers to $2.48$ would logically suggest $3$ as the most fitting option, based on basic rounding principles.

Final Answer

Thus, the correct answer is $3$.