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 :
42:56 :: 110: ?

Options

A. 182
B. 132
C. 136
D. 156

Explanation

To solve the analogy problem \( 42:56 :: 110:? \), we need to identify the relationship between the numbers on the left side of the analogy and apply the same relationship to the number on the right side.

### Step-by-Step Solution:

1. **Identify the relationship between 42 and 56**:
- We can express 42 as \( 6 \times 7 \).
- We can express 56 as \( 7 \times 8 \).
- Here, we see that 42 is the product of 6 and 7, while 56 is the product of 7 and 8. The second number (56) is derived from the first number (42) by multiplying the second factor (7) by the next consecutive integer (8).

2. **Express 110 in a similar form**:
- We can express 110 as \( 10 \times 11 \).
- Here, 10 is the first factor and 11 is the second factor.

3. **Find the next consecutive integer after 11**:
- The next consecutive integer after 11 is 12.

4. **Calculate the product using the next consecutive integer**:
- Now, we multiply the second factor (11) by the next consecutive integer (12):
\[ 11 \times 12 = 132 \]

5. **Conclusion**:
- Therefore, the number that corresponds to 110 in the same relationship as 42 relates to 56 is 132.

### Final Answer:
The answer is \( 132 \).