Identify the odd one out:

The correct option is D6 : G9 : K13.

To find the odd one out, let us analyze the pattern of letters and their numerical positions in the alphabet along with the numbers given in each group:

1. Analyzing the general pattern:
Let us look at the alphabetical positions of the letters:
- A = 1, D = 4, G = 7
- B = 2, E = 5, H = 8
- C = 3, F = 6, I = 9
- D = 4, G = 7, K = 11

Notice that in each term, the letter's alphabetical position is incremented by 3 to get the next letter (e.g., A(1) + 3 = D(4), D(4) + 3 = G(7)).
Also, the number accompanying each letter is equal to its alphabetical position plus 2:
- A(1): 1 + 2 = 3 → A3
- D(4): 4 + 2 = 6 → D6
- G(7): 7 + 2 = 9 → G9

2. Testing each option against this rule:

Option 1: A3 : D6 : G9
- Letters: A(1) → (+3) → D(4) → (+3) → G(7). (Follows +3 pattern)
- Numbers: 1+2=3, 4+2=6, 7+2=9. (Follows +2 pattern)
This group follows the rule.

Option 2: B4 : E7 : H10
- Letters: B(2) → (+3) → E(5) → (+3) → H(8). (Follows +3 pattern)
- Numbers: 2+2=4, 5+2=7, 8+2=10. (Follows +2 pattern)
This group follows the rule.

Option 3: C5 : F8 : I11
- Letters: C(3) → (+3) → F(6) → (+3) → I(9). (Follows +3 pattern)
- Numbers: 3+2=5, 6+2=8, 9+2=11. (Follows +2 pattern)
This group follows the rule.

Option 4: D6 : G9 : K13
- Letters: D(4) → (+3) → G(7) → (+4) → K(11). (Fails +3 pattern, since G to K is +4 instead of +3)
- Numbers: 4+2=6, 7+2=9, 11+2=13.
Since the step from G to K skips 4 positions instead of 3, this group deviates from the pattern.

Therefore, D6 : G9 : K13 is the odd one out.