Which of the following terms will replace the question mark (?) in the given series? KES, MIQ, PMN, TQJ, YUE, ?
- (a)EYY
- (b)EXY
- (c)EXZ
- (d)FYX
Answer
Why
Correct — A. Split the terms into three columns and run each column as its own series.
First letters K, M, P, T, Y = 11, 13, 16, 20, 25 → gaps +2, +3, +4, +5, so the next is +6: 25 + 6 = 31, and 31 − 26 = 5 = E.
Second letters E, I, M, Q, U = 5, 9, 13, 17, 21 → a constant +4: 21 + 4 = 25 = Y.
Third letters S, Q, N, J, E = 19, 17, 14, 10, 5 → gaps −2, −3, −4, −5, so the next is −6: 5 − 6 = −1, which wraps to 25 = Y.
E, Y, Y → option (a).
Why the others are wrong
- (b)EXY — Option (b) is E X Y. Its middle letter X = 24, but the second column climbs by a constant +4 from U = 21, which lands on Y = 25, not X.
- (c)EXZ — Option (c) ends in Z = 26, one place past the required Y. That is the classic wrap error: 5 − 6 = −1 becomes 25 by adding 26, not 26.
- (d)FYX — Option (d) opens with F = 6, which would need a gap of +7 from Y = 25. The first column's gaps grow 2, 3, 4, 5, so the sixth step is +6 and lands on E.
Concept
A three-letter series is three independent series stacked. Split it into columns before looking for anything else — first letters, second letters, third letters — and convert each to alphabet positions.
Here two columns move by a growing gap and one by a constant, so compute every gap in a column before deciding which of the two kinds it is.
Wrapping is the other half of the method. Past Z you subtract 26; before A you add 26. Only the third column wraps here, and an off-by-one in that wrap produces Z instead of Y.
The first and third columns are mirror images of each other: one grows +2, +3, +4, +5 while the other falls −2, −3, −4, −5. Spotting that halves the work.
Key facts
- First letters step +2, +3, +4, +5, so the sixth term steps +6 and reaches E.
- Second letters step a constant +4, taking U to Y.
- Third letters step −2, −3, −4, −5, so the sixth steps −6 from E and wraps to Y.
- Wrapping backwards past A means adding 26, so 5 − 6 = −1 becomes 25 = Y.
Study next
Common traps
- Reading the three columns as one alternating sequence.
- Calling a column constant after checking only its first two gaps.
- Wrapping −1 to Z = 26 instead of Y = 25.
The same mix of a growing-gap column and constant columns is at 9 Sep 2024, 16:00, Reasoning Q.2 — M F T, N I S, P L Q, S O N, W R J, where the first letters step +1, +2, +3, +4 and the answer is B U E.
A version with every column constant is at 12 Sep 2024, 12:30, Reasoning Q.7 (H P L, K L Q, N H V and on), so check the gaps rather than assuming which kind you have.
Related PYQs
No directly related past PYQ was found.