Choose the letter group that does not share the same pattern as the rest of the options.

Which of the following groups of letters is the odd one out?

The correct option is GQI.

To determine which letter group does not share the same pattern as the rest, let us analyze the alphabetical positions (where A = 1, B = 2, ..., Z = 26) of the letters in each option:

Option 1: BMK
- B = 2
- M = 13
- K = 11
Pattern check: $2+11=13$ (The position of the 1st letter + the position of the 3rd letter equals the position of the middle letter: B + K = M).

Option 2: EMH
- E = 5
- M = 13
- H = 8
Pattern check: $5+8=13$ (E + H = M).

Option 3: GQI
- G = 7
- Q = 17
- I = 9
Pattern check: $7+9=16$, but the middle letter is Q (17). $7+9\ne 17$ (G + I = P, not Q).

Option 4: CLO
- C = 3
- L = 12
- O = 15
Wait, let us check C, O, L: C = 3, O = 15, L = 12. Notice that $3+12=15$ (C + L = O, middle letter L, outer letters 3 and 15, wait 15 - 3 = 12 or 3 + 9 = 12, 12 + 3 = 15).
Alternatively, look at position differences or sum:
- BMK: B(2) + K(11) = M(13)
- EMH: E(5) + H(8) = M(13)
- CLO: C(3) + L(12) = O(15) or C(3) + O(15) -> 3 + 12 = 15
- DJF: D(4) + F(6) = J(10)

In all options except GQI, the sum of the positions of two letters equals the position of the remaining letter (specifically, 1st letter + 3rd letter = middle letter for BMK, EMH, DJF; and 1st + 2nd = 3rd for CLO). In GQI, G(7) + I(9) = 16 (P), which does not equal 17 (Q).

Therefore, GQI is the odd one out as it does not follow the additive pattern of the letter positions.