Understanding Letter Group Relation Questions

In this type of question, we are given a set of letter groups that follow a specific hidden rule or logic. Our task is to identify this logic and then find which of the given options contains a letter group that follows the exact same rule.

Analyzing the Given Letter Group: (TOPX, ZVXG, FCFP)

Let's examine the relationship between the letters within this group. The question states that the letters of each group are related with the letters of the same group. This often implies a relationship between corresponding letters across the words in the group.

We can assign numerical values to each letter based on its position in the English alphabet (A=1, B=2, ..., Z=26).

Now, let's look for a pattern by comparing the letters at the same position across the three words:

• 1st Letters: T (20), Z (26), F (6)
  • From T to Z: \(26 - 20 = +6\).
  • From Z to F: \(6 - 26 = -20\). Considering the alphabet is cyclical, \(26 + 6 = 32\), so \(32 - 26 = 6\). This means \(+6\).
  • The pattern for the 1st letters is \(+6\).
• 2nd Letters: O (15), V (22), C (3)
  • From O to V: \(22 - 15 = +7\).
  • From V to C: \(3 - 22 = -19\). Cyclically, \(22 + 7 = 29\), so \(29 - 26 = 3\). This means \(+7\).
  • The pattern for the 2nd letters is \(+7\).
• 3rd Letters: P (16), X (24), F (6)
  • From P to X: \(24 - 16 = +8\).
  • From X to F: \(6 - 24 = -18\). Cyclically, \(24 + 8 = 32\), so \(32 - 26 = 6\). This means \(+8\).
  • The pattern for the 3rd letters is \(+8\).
• 4th Letters: X (24), G (7), P (16)
  • From X to G: \(7 - 24 = -17\). Cyclically, \(24 + 9 = 33\), so \(33 - 26 = 7\). This means \(+9\).
  • From G to P: \(16 - 7 = +9\).
  • The pattern for the 4th letters is \(+9\).

The identified logic/rule/relation is that the corresponding letters in the three words follow a positional increment of \(+6\), \(+7\), \(+8\), and \(+9\) respectively, considering the alphabet as cyclical.

Checking the Options for the Same Logic

Option 1: (KQRN, QXZW, WEHF)

• 1st Letters: K (11), Q (17), W (23)
  • K to Q: \(17 - 11 = +6\).
  • Q to W: \(23 - 17 = +6\).
  • Pattern: \(+6\). Matches the rule.
• 2nd Letters: Q (17), X (24), E (5)
  • Q to X: \(24 - 17 = +7\).
  • X to E: \(5 - 24 = -19\). Cyclically, \(24 + 7 = 31\), \(31 - 26 = 5\). This means \(+7\).
  • Pattern: \(+7\). Matches the rule.
• 3rd Letters: R (18), Z (26), H (8)
  • R to Z: \(26 - 18 = +8\).
  • Z to H: \(8 - 26 = -18\). Cyclically, \(26 + 8 = 34\), \(34 - 26 = 8\). This means \(+8\).
  • Pattern: \(+8\). Matches the rule.
• 4th Letters: N (14), W (23), F (6)
  • N to W: \(23 - 14 = +9\).
  • W to F: \(6 - 23 = -17\). Cyclically, \(23 + 9 = 32\), \(32 - 26 = 6\). This means \(+9\).
  • Pattern: \(+9\). Matches the rule.

Option 1 follows the exact same \(+6\), \(+7\), \(+8\), \(+9\) pattern across the corresponding letters of the three words.

Option 2: (LPCR, RWKZ, XDSI)

Checking the 4th letters: R (18), Z (26), I (9). R to Z is \(26-18=+8\). Z to I is \(9-26=-17\). Cyclically, \(26+9=35\), \(35-26=9\). This means \(+9\). The pattern for 4th letters is \(+8\) then \(+9\), not consistently \(+9\). Option 2 does not follow the rule.

Option 3: (AJNP, GQVY, MXEH)

Checking the 3rd letters: N (14), V (22), E (5). N to V is \(22-14=+8\). V to E is \(5-22=-17\). Cyclically, \(22+9=31\), \(31-26=5\). This means \(+9\). The pattern for 3rd letters is \(+8\) then \(+9\), not consistently \(+8\). Option 3 does not follow the rule.

Option 4: (TGPA, ZNXJ, EUFS)

Checking the 1st letters: T (20), Z (26), E (5). T to Z is \(26-20=+6\). Z to E is \(5-26=-21\). Cyclically, \(26+5=31\), \(31-26=5\). This means \(+5\). The pattern for 1st letters is \(+6\) then \(+5\), not consistently \(+6\). Option 4 does not follow the rule.

Conclusion

Based on the analysis, only Option 1 (KQRN, QXZW, WEHF) follows the same pattern of adding \(+6\), \(+7\), \(+8\), and \(+9\) cyclically to the corresponding letters of the three words as observed in the given group (TOPX, ZVXG, FCFP).

Revision Table: Letter Pattern Analysis

Additional Information: Alphabetical Positional Values

Understanding the numerical position of each letter in the alphabet is crucial for solving these types of logic and reasoning questions. When the patterns involve adding or subtracting, remembering that the alphabet 'wraps around' (after Z comes A) is important for cyclical patterns.

A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8, I = 9, J = 10, K = 11, L = 12, M = 13, N = 14, O = 15, P = 16, Q = 17, R = 18, S = 19, T = 20, U = 21, V = 22, W = 23, X = 24, Y = 25, Z = 26.

When adding, if the value exceeds 26, subtract 26 to find the corresponding letter. For example, Z + 8 = 26 + 8 = 34. \(34 - 26 = 8\), which corresponds to H.

When subtracting, if the value goes below 1, add 26. For example, C - 4 = 3 - 4 = -1. \(-1 + 26 = 25\), which corresponds to Y.