Choose the set of numbers from the four alternatives which is similar to the given set.
Given set : (9, 15, 21)

Options

A. (10, 14, 16)
B. (7, 21, 28)
C. (5, 10, 25)
D. (4, 8, 12)

Explanation

To solve the problem of finding a set of numbers similar to the given set (9, 15, 21), we will analyze the relationship between the numbers in the given set and then check each option to see if it follows the same pattern.

### Step-by-Step Solution:

1. **Identify the Given Set**:
The given set is (9, 15, 21).

2. **Determine the Relationship**:
We notice that the first number (9) and the third number (21) can be added together:
\[ 9 + 21 = 30 \]
Now, we find the average of these two numbers:
\[ \text{Average} = \frac{30}{2} = 15 \]
The middle number (15) is indeed the second number in the given set.

3. **Check Each Option**:
We will now check each of the four options to see if they follow the same pattern.

- **Option 1**: (10, 14, 16)
- Calculate the average:
\[ 10 + 16 = 26 \quad \text{and} \quad \frac{26}{2} = 13 \]
- 13 is not equal to 14, so option 1 is eliminated.

- **Option 2**: (7, 21, 28)
- Calculate the average:
\[ 7 + 28 = 35 \quad \text{and} \quad \frac{35}{2} = 17.5 \]
- 17.5 is not equal to 21, so option 2 is eliminated.

- **Option 3**: (5, 10, 25)
- Calculate the average:
\[ 5 + 25 = 30 \quad \text{and} \quad \frac{30}{2} = 15 \]
- 15 is not equal to 10, so option 3 is eliminated.

- **Option 4**: (4, 8, 12)
- Calculate the average:
\[ 4 + 12 = 16 \quad \text{and} \quad \frac{16}{2} = 8 \]
- 8 is equal to the middle number (8), so option 4 follows the same pattern.

4. **Conclusion**:
The only option that maintains the same relationship as the given set is option 4: (4, 8, 12).

### Final Answer:
The correct option is **(4, 8, 12)**.

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