6:15:: 35:?

Options

A. 63
B. 77
C. 81
D. 110

Explanation

To solve the analogy problem \(6:15::35:?\), we need to find the number that corresponds to 35 in the same way that 15 corresponds to 6.

### Step-by-Step Solution:

1. **Identify the relationship in the first pair (6 and 15):**
- We can express 6 as \(2 \times 3\).
- We can express 15 as \(3 \times 5\).
- Here, we see that the second number (15) can be derived from the first number (6) by multiplying it by a factor that includes one of its factors (3).

2. **Express the second pair (35 and ?):**
- We can express 35 as \(5 \times 7\).
- We need to find a number that can be expressed in a similar way to 15, using the factors of 35.

3. **Finding the corresponding number:**
- The factors of 35 are 5 and 7. We need to find a number that can be formed using these factors.
- If we consider the factor 7, we can multiply it by 9 to get 63, which is \(7 \times 9\).
- However, we need to check if there is a more suitable option that matches the analogy.

4. **Check the options:**
- We need to find a number that is related to 35 in a similar way that 15 is related to 6.
- The number 77 can be expressed as \(7 \times 11\), which uses one of the factors of 35 (7) and introduces a new factor (11).

5. **Conclusion:**
- Therefore, the answer to the analogy \(6:15::35:?\) is \(77\).

### Final Answer:
The value of the question mark is \(77\).

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