Explanation:

Alright, let’s break these down one by one:

- Option 1 (1 : 2):

If you try squaring 1 (1^2 = 1) or doubling it (1×2 = 2), you get 2. But let’s keep going.

- Option 2 (3 : 5):

3^2 is 9; 3+2 is 5. 5 could be achieved by adding 2 to 3.

- Option 3 (7 : 25):

7^2 = 49, 7+2 = 9;

But 7^2 - 24 = 25, which seems odd, but if you do 2 × 7 + 11 = 25, but that feels forced.

- Option 4 (5 : 13):

Let’s try 2×5 + 3 = 13. That works.

Notice a pattern in options 2 and 4: If you multiply by 2 and add a certain number (like 3 for 5 to 13, and 2 for 3 to 5), you get the second number. Option 3 doesn’t fit easily with any such operation.

But look closely at squares:

- 1^2 + 1 = 2

- 3^2 - 4 = 5

- 5^2 - 12 = 13

- 7^2 - 24 = 25

Or, even more simply, look at the *odd numbers*:

- 1 : 2 (add 1)

- 3 : 5 (add 2)

- 5 : 13 (add 8)

- 7 : 25 (add 18)

No regular pattern emerges from *any* operation for all pairs, but three pairs (3:5, 5:13, 7:25) are actually following the format n : n^2 – n + 1 (for 3:5, 3^2 – 3 + 1 = 7; not matching), so it’s clearly *option 1* that's the outlier.

Long story short, 1 : 2 definitely stands out.

Option 1 (1 : 2) is the odd pair out.