Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the one that is different.

Question

Prepp Team · Accepted Answer

Analyzing Letter Cluster Patterns in Reasoning Questions

This question asks us to identify the letter cluster that is different from the other three. These types of problems, known as 'Odd One Out' or 'Classification', test our ability to find a common pattern or rule that applies to a majority of the items and then identify the item that does not follow that rule.

Understanding the Pattern in Letter Clusters

Letter cluster or letter series questions often rely on the positional value of letters in the English alphabet. The pattern can involve:

Differences between the positions of consecutive letters.
Sum or product of positional values.
Skipping letters in a sequence.
Vowel/Consonant patterns.
Reverse alphabetical order.

In this specific question, let's examine the differences between the alphabetical positions of the letters in each cluster.

We assign numerical positions to each letter, starting with A=1, B=2, ..., Z=26.

Letter	Position
A	1
B	2
C	3
E	5
F	6
J	10
N	14
P	16
Q	17
R	18
U	21
Y	25

Analyzing Each Letter Cluster

Let's analyze the relationship between the letters in each given cluster by looking at the backward difference in their alphabetical positions, considering wrapping around from A to Z.

Option 1: YJB

From Y to J: Position of Y is 25, Position of J is 10. The backward difference is $25 - 10 = 15$.
From J to B: Position of J is 10, Position of B is 2. The backward difference is $10 - 2 = 8$.
Pattern for YJB: -15, -8 backward steps.

Option 2: UFQ

From U to F: Position of U is 21, Position of F is 6. The backward difference is $21 - 6 = 15$.
From F to Q: Position of F is 6, Position of Q is 17. Since $6 < 17$, we wrap around. The backward steps are $6 \to 5 \to ... \to 1 \to 26 \to ... \to 17$. The number of steps is $(6-1) + 1 + (26-17) = 5 + 1 + 9 = 15$. Alternatively, using modular arithmetic: $(6 - 15) \pmod{26} = -9 \pmod{26} = 17$. Position 17 is Q. The backward difference is 15.
Pattern for UFQ: -15, -15 backward steps.

Option 3: RCN

From R to C: Position of R is 18, Position of C is 3. The backward difference is $18 - 3 = 15$.
From C to N: Position of C is 3, Position of N is 14. Wrapping around: $(3 - 15) \pmod{26} = -12 \pmod{26} = 14$. Position 14 is N. The backward difference is 15.
Pattern for RCN: -15, -15 backward steps.

Option 4: EPA

From E to P: Position of E is 5, Position of P is 16. Wrapping around: $(5 - 15) \pmod{26} = -10 \pmod{26} = 16$. Position 16 is P. The backward difference is 15.
From P to A: Position of P is 16, Position of A is 1. The backward difference is $16 - 1 = 15$.
Pattern for EPA: -15, -15 backward steps.

Identifying the Different Letter Cluster

Comparing the patterns:

UFQ follows a -15, -15 backward steps pattern.
RCN follows a -15, -15 backward steps pattern.
EPA follows a -15, -15 backward steps pattern.
YJB follows a -15, -8 backward steps pattern.

Three of the letter clusters (UFQ, RCN, EPA) share the same pattern of a backward difference of 15 between consecutive letters, wrapping around the alphabet. The letter cluster YJB does not follow this pattern for the second pair of letters (J to B).

Letter Cluster Pattern Revision Table

Cluster	Letter Positions	Difference 1 (L1 to L2)	Difference 2 (L2 to L3)	Pattern Match
YJB	25, 10, 2	$25 - 10 = 15$	$10 - 2 = 8$	-15, -8
UFQ	21, 6, 17	$21 - 6 = 15$	$(6 - 15) \pmod{26} = 17$ (15 steps back)	-15, -15
RCN	18, 3, 14	$18 - 3 = 15$	$(3 - 15) \pmod{26} = 14$ (15 steps back)	-15, -15
EPA	5, 16, 1	$(5 - 15) \pmod{26} = 16$ (15 steps back)	$16 - 1 = 15$	-15, -15

Based on this analysis, YJB is the cluster that is different from the others.

Additional Information on Letter Series Questions

Letter series and letter cluster problems are common in logical reasoning sections of competitive exams. To solve them effectively, practice recognizing various patterns:

Consecutive Differences: The difference in alphabetical position between adjacent letters is constant or follows a sequence (e.g., +2, +3, +4).
Alternating Patterns: Different patterns apply to alternate letters or pairs of letters.
Skipping Letters: A fixed number of letters are skipped between consecutive letters.
Vowel/Consonant Grouping: The series might group vowels or consonants in a specific order or pattern.
Sum/Product of Positions: The sum or product of the positional values might follow a pattern.
Reverse Order: The pattern might be based on reverse alphabetical order (Z=1, Y=2, etc.).

Always check for simple arithmetic progressions or constant differences first, both forwards and backwards, and consider wrapping around the alphabet.