If 'a' and 'b' are two distinct prime numbers lying between 1 and 10, which of the following can be the sum of 'a' and 'b'-

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem of finding the possible sums of two distinct prime numbers 'a' and 'b' that lie between 1 and 10, we can follow these steps:

### Step 1: Identify the prime numbers between 1 and 10
The prime numbers between 1 and 10 are:
- 2
- 3
- 5
- 7

### Step 2: Calculate the sums of all distinct pairs of prime numbers
Now, we will calculate the sums of all distinct pairs of these prime numbers:

1. **Pair (2, 3)**:
- Sum = 2 + 3 = 5
2. **Pair (2, 5)**:
- Sum = 2 + 5 = 7
3. **Pair (2, 7)**:
- Sum = 2 + 7 = 9
4. **Pair (3, 5)**:
- Sum = 3 + 5 = 8
5. **Pair (3, 7)**:
- Sum = 3 + 7 = 10
6. **Pair (5, 7)**:
- Sum = 5 + 7 = 12

### Step 3: List all the distinct sums calculated
From the calculations above, the distinct sums of the pairs are:
- 5
- 7
- 8
- 9
- 10
- 12

### Step 4: Identify the valid sums based on the options provided
Assuming the options given in the question are 5, 6, 7, 8, and 9, we can check which of these sums are valid:
- **5**: Yes, from the pair (2, 3)
- **6**: No, there is no pair that sums to 6
- **7**: Yes, from the pair (2, 5)
- **8**: Yes, from the pair (3, 5)
- **9**: Yes, from the pair (2, 7)

### Conclusion
The valid sums of 'a' and 'b' that can be formed by distinct prime numbers between 1 and 10 are **5, 7, 8, and 9**.

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