Express each of the following numbers as the sum of two odd primes .
(i) 36, (ii) 42, (iii) 84, (iv) 98

Answer

To express each of the given numbers as the sum of two odd primes, we will follow these steps:

### Step-by-Step Solution

**(i) Expressing 36 as the sum of two odd primes:**
1. Identify odd prime numbers less than 36. The odd prime numbers are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.
2. Check combinations of these primes to see which pair sums to 36.
3. After testing combinations, we find that:
- 7 + 29 = 36
4. Therefore, 36 can be expressed as the sum of two odd primes: **7 + 29**.

**(ii) Expressing 42 as the sum of two odd primes:**
1. Again, use the list of odd prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41.
2. Check combinations to find a pair that sums to 42.
3. After testing combinations, we find that:
- 5 + 37 = 42
4. Thus, 42 can be expressed as the sum of two odd primes: **5 + 37**.

**(iii) Expressing 84 as the sum of two odd primes:**
1. Use the odd prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83.
2. Check combinations to find a pair that sums to 84.
3. After testing combinations, we find that:
- 17 + 67 = 84
4. Therefore, 84 can be expressed as the sum of two odd primes: **17 + 67**.

**(iv) Expressing 98 as the sum of two odd primes:**
1. Again, use the list of odd prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
2. Check combinations to find a pair that sums to 98.
3. After testing combinations, we find that:
- 79 + 19 = 98
4. Thus, 98 can be expressed as the sum of two odd primes: **79 + 19**.

### Final Results
- (i) 36 = 7 + 29
- (ii) 42 = 5 + 37
- (iii) 84 = 17 + 67
- (iv) 98 = 79 + 19