Explanation:

Let's break down the number-pairs and look for a pattern:

- Option 1: 18 : 42

- Option 2: 1 : 6

- Option 3: 5 : 34

- Option 4: 7 : 18

Let’s try multiplying the first number by the next integer and see:

- 18 × 3 = 54 (not 42)

- 1 × 2 = 2 (not 6)

- 5 × 6 = 30 (not 34)

- 7 × 8 = 56 (not 18)

Instead, try the pattern n² + n:

- 18² + 18 = 324 + 18 = 342

- 1² + 1 = 1 + 1 = 2

- 5² + 5 = 25 + 5 = 30

- 7² + 7 = 49 + 7 = 56

No, doesn't fit. Let's try n × n + 1:

- 18 × 19 = 342

- 1 × 2 = 2

- 5 × 6 = 30

- 7 × 8 = 56

Still not matching. Now, try n × n - 2:

- 18 × 16 = 288

- 1 × (1 - 2) = -1

- 5 × 3 = 15

- 7 × 5 = 35

No. Now try n³ - 2:

- 18³ - 2 = way beyond 42

Now, try: 2 × n² + 2

- 2 × 18² + 2 = 2 × 324 + 2 = 650

- 2 × 1² + 2 = 2 × 1 + 2 = 4

- 2 × 5² + 2 = 2 × 25 + 2 = 52

- 2 × 7² + 2 = 2 × 49 + 2 = 100

None matches.

Let’s check each pair by noticing another operation, maybe adding a number, or looking for what can give these results:

Now try n² - 2n:

- 18² - 36 = 324 - 36 = 288

- 1² - 2= -1

- 25 - 10 = 15

- 49 - 14 = 35

None fits. Now, let’s try n² + n + n, i.e., n² + 2n

- 18² + 36 = 324 + 36 = 360

- 1 + 2 = 3

- 25 + 10 = 35

- 49 + 14 = 63

Let’s see by multiplying by different integers:

Option 2: 1 : 6

Try 1 × 6 = 6 ?

Option 3: 5 : 34

5 × 6 = 30, 5 × 7 = 35 ? maybe 5 × 7 - 1 = 34

Option 4: 7 : 18

7 × 2 = 14, 7 × 3 = 21, 18 ÷ 7 ˜ 2.57

Option 1: 18 : 42

18 × 2 = 36, 18 × 3 = 54, 42 ÷ 18 = 2.33

Or maybe, the pattern is n × n + 1 (i.e., number × next number):

Option 2: 1 × 2 = 2

Option 3: 5 × 6 = 30

Option 4: 7 × 8 = 56

Option 1: 18 × 19 = 342

So, the odd pair is the one that does not fit the pattern (number × next number).

- 1 × 2 = 2 (not 6)

- 5 × 6 = 30 (not 34)

- 7 × 8 = 56 (not 18)

- 18 × 19 = 342 (not 42)

But none of them fit, except maybe option 2, if you try 1 + 5 = 6.

Try if the operation is n + 5:

- 1 + 5 = 6 ?

- 5 + 29 = 34

- 7 + 11 = 18

- 18 + 24 = 42

Now, check n × n - 1:

- 1 × 0 = 0

- 5 × 4 = 20

- 7 × 6 = 42

- 18 × 17 = 306

Still not fitting.

Now, check this pattern: 2n + 4

- 1 × 2 + 4 = 2 + 4 = 6 ?

- 5 × 2 + 4 = 10 + 4 = 14

- 7 × 2 + 4 = 14 + 4 = 18 ?

- 18 × 2 + 4 = 36 + 4 = 40

So Options 2 and 4 fit 2n + 4.

Therefore, the odd pairs are Option 1 and Option 3! Among the given choices, the best fit seems Option 3: 5 : 34.

So,

- Option 2: 1 : 6 ? 1 × 2 + 4 = 6

- Option 4: 7 : 18 ? 7 × 2 + 4 = 18

- But Option 3: 5 : 34 does not fit; 5 × 2 + 4 = 14, or 5 × 7 -1 = 34

- Option 1: 18 × 2 + 4 = 40 (not 42)

So, 34 is the only number achieved with 5 × 7 - 1 = 34, a distinctly different operation.

Hence, the odd one is Option 3: 5 : 34

- Patterns in options 2 and 4: 2n + 4

- Option 3: Seems to use n × (n + 2) - 1

- Option 1: Doesn't fit the pattern but is closer than option 3

So, the correct answer is:

Option 3: 5 : 34