In the questions, there is a certain relationship between the two given numbers on one side of :: and one number is given on another side of :: . It is required to find another number from the given alternative having the same relationship with this number as the numbers of the given pair has :
68 : 130 :: ?: 350

Options

A. 210
B. 216
C. 222
D. 240

Explanation

To solve the analogy problem given, we need to identify the relationship between the numbers 68 and 130, and then apply that same relationship to find the missing number that relates to 350.

### Step-by-Step Solution:

1. **Identify the relationship between 68 and 130:**
- We notice that 68 can be expressed as \(4^3 + 4\).
- Calculation: \(4^3 = 64\) and \(64 + 4 = 68\).
- Similarly, for 130, we can express it as \(5^3 + 5\).
- Calculation: \(5^3 = 125\) and \(125 + 5 = 130\).
- Thus, the relationship can be summarized as:
- For the first number \(n\), \(n^3 + n\).

2. **Determine the next number in the sequence:**
- The first number (4) is followed by the next consecutive number (5).
- Therefore, we can infer that the next number we will use for 350 will be 6 (the next consecutive number after 5).

3. **Apply the same relationship to find the missing number:**
- For the number related to 350, we will use \(6\):
- Calculation: \(6^3 + 6\).
- First, calculate \(6^3\):
- \(6^3 = 216\).
- Now, add \(6\) to it:
- \(216 + 6 = 222\).

4. **Conclusion:**
- The missing number that relates to 350 in the same way that 68 relates to 130 is **222**.

### Final Answer:
The answer is **222**.