Which of the following letter-clusters will replace the question mark (?) in the given series to make it logically complete? NUT, RYX, VCB, ZGF, ?
- (a)DKJ
- (b)EKJ
- (c)EKL
- (d)DKL
Answer
Why
Correct — A. Convert each cluster to alphabet positions and read the three columns downwards.
Rule: every column advances +4, with the alphabet wrapping past Z back to A.
First letters: N(14) → R(18) → V(22) → Z(26) → 30 − 26 = 4 = D
Second letters: U(21) → Y(25) → C(29) → G(33) → 37 − 26 = 11 = K
Third letters: T(20) → X(24) → B(28) → F(32) → 36 − 26 = 10 = J
The fifth cluster is DKJ — option (a).
Why the others are wrong
- (b)EKJ — Option (b) has the last two letters right but opens with E, which is a +5 step from Z. Z is 26, and 26 + 4 = 30 wraps to 4, giving D.
- (c)EKL — Option (c) misses twice — E for the first letter, a +5 step, and L for the third, which is +6 from F. The series moves +4 in every column.
- (d)DKL — Option (d) gets D and K, then puts L third. F is 6 and 6 + 4 = 10, which is J, so the +4 rule fails in the last column.
Concept
Letter-cluster series are alphabet arithmetic. Write A = 1 through Z = 26, turn each cluster into three numbers, and the pattern usually shows up as a constant step in each column.
Here all three columns move +4, which is why the clusters look scattered to the eye. NUT, RYX and VCB say nothing, while 14-21-20, 18-25-24 and 22-29-28 are plainly regular.
The wrap is the only technical point. Past 26, subtract 26 — so 29 is C, 33 is G and 37 is K.
The paper's own clusters start wrapping at the third term, VCB, not at the answer. A candidate who has not learned to subtract 26 will stall while checking the given series, long before reaching the blank.
Key facts
- A is 1 and Z is 26, and any step past 26 wraps by subtracting 26.
- Every column of NUT, RYX, VCB and ZGF advances by exactly 4.
- The fifth term comes from 30, 37 and 36, which reduce to 4, 11 and 10 — D, K and J.
Study next
Common traps
- Counting the wrap as +5 instead of +4 and writing E where D belongs
- Getting two columns right and stopping, when all three have to agree
- Reading the clusters as words and hunting for meaning instead of converting to numbers
The step size and the number of columns change from shift to shift, so convert first and look for the pattern afterwards.
The same alphabet arithmetic decides this paper's odd-one-out — also asked 10 Sep 2024, 16:00, Reasoning Q.22.
Related PYQs
No directly related past PYQ was found.