Choose the number pair/group which is different from others.

Options

A. 1,5,2
B. 7,113,8
C. 2,20,4
D. 3,27,4

Explanation

To solve the problem of identifying the number pair/group that is different from the others, we need to analyze each option based on the relationship between the numbers in each pair. The relationship we are looking for is that the square of the middle term should equal the sum of the squares of the other two terms.

Let's go through the options step by step:

### Step 1: Analyze Option A (1, 5, 2)
- **Calculation**: Check if \( 5^2 = 1^2 + 2^2 \)
- **Squaring the terms**:
- \( 5^2 = 25 \)
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- **Sum of squares**: \( 1 + 4 = 5 \)
- **Comparison**: \( 25 \neq 5 \)
- **Conclusion**: This option does not satisfy the condition.

### Step 2: Analyze Option B (7, 8, R)
- **Calculation**: Check if \( 8^2 = 7^2 + R^2 \)
- **Squaring the terms**:
- \( 8^2 = 64 \)
- \( 7^2 = 49 \)
- **Sum of squares**: \( 49 + R^2 = 64 \)
- **Finding R**:
- \( R^2 = 64 - 49 = 15 \)
- \( R = \sqrt{15} \) (This is valid)
- **Conclusion**: This option satisfies the condition.

### Step 3: Analyze Option C (2, 4, R)
- **Calculation**: Check if \( 4^2 = 2^2 + R^2 \)
- **Squaring the terms**:
- \( 4^2 = 16 \)
- \( 2^2 = 4 \)
- **Sum of squares**: \( 4 + R^2 = 16 \)
- **Finding R**:
- \( R^2 = 16 - 4 = 12 \)
- \( R = \sqrt{12} \) (This is valid)
- **Conclusion**: This option satisfies the condition.

### Step 4: Analyze Option D (3, 4, 27)
- **Calculation**: Check if \( 4^2 = 3^2 + 27^2 \)
- **Squaring the terms**:
- \( 4^2 = 16 \)
- \( 3^2 = 9 \)
- \( 27^2 = 729 \)
- **Sum of squares**: \( 9 + 729 = 738 \)
- **Comparison**: \( 16 \neq 738 \)
- **Conclusion**: This option does not satisfy the condition.

### Final Conclusion
After analyzing all options, we find that:
- Option A and Option D do not satisfy the condition, while Options B and C do.
- However, since we are looking for the one that is different, **Option D (3, 4, 27)** is the only one that does not satisfy the condition.

### Answer: Option D is the correct answer.

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