Choosing a similarly related pair as the given number pair on the basis of the relation between the numbers in each pair .
12 : 169 : : ? : ?

Options

A. ` 7 : 50`
B. `11 : 144`
C. `15 : 240`
D. `5 : 49`

Explanation

To solve the analogy problem given, we need to identify the relationship between the numbers in the pair 12 and 169, and then apply that same relationship to find the corresponding pair.

### Step-by-Step Solution:

1. **Identify the relationship between the numbers 12 and 169.**
- The number 169 can be expressed as \(12 + 1\) squared.
- Calculation: \(12 + 1 = 13\) and \(13^2 = 169\).

2. **Establish the formula based on the identified relationship.**
- If we denote the first number in the new pair as \(x\), then the second number should be \( (x + 1)^2 \).
- This means for any number \(x\), the second number will be the square of \(x + 1\).

3. **Test possible values for \(x\) to find a suitable pair.**
- Let's try \(x = 7\):
- \(7 + 1 = 8\) and \(8^2 = 64\). So the pair would be \(7 : 64\).
- Next, try \(x = 11\):
- \(11 + 1 = 12\) and \(12^2 = 144\). So the pair would be \(11 : 144\).
- Continue testing other values:
- For \(x = 15\): \(15 + 1 = 16\) and \(16^2 = 256\), giving \(15 : 256\).
- For \(x = 5\): \(5 + 1 = 6\) and \(6^2 = 36\), giving \(5 : 36\).

4. **Compare the results with the options provided.**
- The pairs we found are \(7 : 64\), \(11 : 144\), \(15 : 256\), and \(5 : 36\).
- Among these, the pair \(11 : 144\) matches one of the options provided.

5. **Conclusion:**
- The correct answer to the analogy is \(11 : 144\).

### Final Answer:
The answer is \(11 : 144\).