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 :
182:?:: 210: 380

Options

A. 156
B. 240
C. 272
D. 342

Explanation

To solve the analogy problem, we need to find the relationship between the numbers given in the pairs. The question is structured as follows:

182 : ? :: 210 : 380

### Step-by-Step Solution:

1. **Identify the Relationship in the Second Pair (210 : 380)**:
- We need to find a mathematical relationship between 210 and 380.
- Let's express 210 in terms of its factors:
- 210 = 14 × 15
- Now, we can express 380:
- 380 = 19 × 20

2. **Analyze the Relationship**:
- Notice that 14 and 15 are consecutive integers, and their product is 210.
- Similarly, 19 and 20 are also consecutive integers, and their product is 380.

3. **Determine the Pattern**:
- The pattern observed is that the first number (210) is the product of two consecutive integers, and the second number (380) is the product of the next two consecutive integers after adding 4 to the larger integer of the first pair.
- Specifically, if we take 14 (the smaller integer of the first pair), we add 4 to the larger integer (15), resulting in 19 (15 + 4).

4. **Apply the Same Pattern to the First Pair (182 : ?)**:
- Now, we need to express 182 in terms of its factors:
- 182 = 13 × 14
- Following the same pattern, we look for the next consecutive integers after adding 4 to the larger integer of this pair:
- The larger integer here is 14. Adding 4 gives us 18.
- The next consecutive integer after 18 is 19.

5. **Calculate the Product**:
- Now, we calculate the product of 18 and 19:
- 18 × 19 = 342

6. **Conclusion**:
- Therefore, the number that corresponds to 182 in the analogy is 342.

### Final Answer:
182 : 342 :: 210 : 380