Choose the set of numbers from the four alternatives which is similar to the given set.
Given set : (21, 51, 15)

Options

A. (21, 30, 51)
B. (21, 35, 41)
C. (31, 51, 42)
D. (21, 91, 35)

Explanation

To solve the problem, we need to find a set of numbers that follows the same pattern as the given set (21, 51, 15). Let's break down the steps to identify the correct option.

### Step-by-Step Solution:

1. **Identify the Relationship in the Given Set:**
- The given set is (21, 51, 15).
- Here, 51 is the middle number, and we need to find a pattern that connects 21 and 15 to 51.
- Notice that 51 can be derived from 21 and 15 using a specific operation.

2. **Establish a Pattern:**
- We can observe that if we multiply the third number (15) by 2 and then add the first number (21), we can reach the middle number (51).
- Calculation: \( 15 \times 2 + 21 = 30 + 21 = 51 \).

3. **Apply the Same Pattern to Each Option:**
- We will apply the same operation (multiply the third number by 2 and then add the first number) to each of the options provided.

4. **Check Each Option:**
- **Option 1: (21, 30, 51)**
- Calculation: \( 51 \times 2 + 21 = 102 + 21 = 123 \) (not equal to 30).
- **Option 2: (21, 35, 41)**
- Calculation: \( 41 \times 2 + 21 = 82 + 21 = 103 \) (not equal to 35).
- **Option 3: (31, 51, 42)**
- Calculation: \( 42 \times 2 + 31 = 84 + 31 = 115 \) (not equal to 51).
- **Option 4: (21, 91, 35)**
- Calculation: \( 35 \times 2 + 21 = 70 + 21 = 91 \) (equal to 91).

5. **Conclusion:**
- The only option that follows the same pattern as the given set is **Option 4: (21, 91, 35)**.

### Final Answer:
The correct option is **Option 4: (21, 91, 35)**.