Analyzing Letter Sets for the Odd One Out

The question asks us to identify the unique set of letters among the given options. To do this, we need to find a common pattern that unites three of the sets and distinguishes the fourth one. The pattern often relates to the position of letters in the alphabet and the numerical gaps between them.

Understanding Alphabetical Sequence Patterns

Let's examine each set by assigning numerical positions to the letters based on their order in the English alphabet (A=1, B=2, C=3, and so on) and calculating the difference (gap) between consecutive letters.

• Set 1: EFHK
  • E is the 5th letter.
  • F is the 6th letter.
  • H is the 8th letter.
  • K is the 11th letter.
  Calculating the gaps between consecutive letters:
  • Gap 1 (E to F): Position of F $-$ Position of E = $6 - 5 = 1$
  • Gap 2 (F to H): Position of H $-$ Position of F = $8 - 6 = 2$
  • Gap 3 (H to K): Position of K $-$ Position of H = $11 - 8 = 3$
  The sequence of gaps for EFHK is 1, 2, 3.
• Set 2: ABCG
  • A is the 1st letter.
  • B is the 2nd letter.
  • C is the 3rd letter.
  • G is the 7th letter.
  Calculating the gaps between consecutive letters:
  • Gap 1 (A to B): Position of B $-$ Position of A = $2 - 1 = 1$
  • Gap 2 (B to C): Position of C $-$ Position of B = $3 - 2 = 1$
  • Gap 3 (C to G): Position of G $-$ Position of C = $7 - 3 = 4$
  The sequence of gaps for ABCG is 1, 1, 4.
• Set 3: QRTW
  • Q is the 17th letter.
  • R is the 18th letter.
  • T is the 20th letter.
  • W is the 23rd letter.
  Calculating the gaps between consecutive letters:
  • Gap 1 (Q to R): Position of R $-$ Position of Q = $18 - 17 = 1$
  • Gap 2 (R to T): Position of T $-$ Position of R = $20 - 18 = 2$
  • Gap 3 (T to W): Position of W $-$ Position of T = $23 - 20 = 3$
  The sequence of gaps for QRTW is 1, 2, 3.
• Set 4: MNPS
  • M is the 13th letter.
  • N is the 14th letter.
  • P is the 16th letter.
  • S is the 19th letter.
  Calculating the gaps between consecutive letters:
  • Gap 1 (M to N): Position of N $-$ Position of M = $14 - 13 = 1$
  • Gap 2 (N to P): Position of P $-$ Position of N = $16 - 14 = 2$
  • Gap 3 (P to S): Position of S $-$ Position of P = $19 - 16 = 3$
  The sequence of gaps for MNPS is 1, 2, 3.

Identifying the Different Letter Set Pattern

By comparing the gap sequences we found:

• EFHK has gaps: 1, 2, 3
• ABCG has gaps: 1, 1, 4
• QRTW has gaps: 1, 2, 3
• MNPS has gaps: 1, 2, 3

We can see that three sets – EFHK, QRTW, and MNPS – share a common pattern where the gap between consecutive letters increases sequentially (1, 2, 3). The set ABCG follows a different pattern (1, 1, 4).

Conclusion on the Different Set

Therefore, the set ABCG is the one that is different from the others based on the established alphabetical gap pattern.