A series is given with one term missing. Select the correct alternative from…
2024
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series. NRCH, IYNJ, FJUE, AQFB, ?
Answer: A. XBMW — Concept. In an alphabet series whose terms are blocks of letters, replace every letter by its position in the alphabet (A = 1, B = 2, …, Z = 26) and measure…
- A.
XBMW
- B.
QRST
- C.
XTQR
- D.
XMNO
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Show answer & explanation
Correct answer: A
Concept. In an alphabet series whose terms are blocks of letters, replace every letter by its position in the alphabet (A = 1, B = 2, …, Z = 26) and measure the shift from one term to the matching letter of another term, wrapping past Z round to A. When consecutive terms show no single steady shift, the standard next move is to compare each term with the term two places earlier, because many alphabet series interleave two progressions rather than running one.
Application.
Write the terms as position numbers: NRCH = 14, 18, 3, 8; IYNJ = 9, 25, 14, 10; FJUE = 6, 10, 21, 5; AQFB = 1, 17, 6, 2.
Compare the 2nd term with the 4th term, IYNJ with AQFB: 9 → 1, 25 → 17, 14 → 6, 10 → 2. Every one of the four letters has moved back by exactly 8.
So the rule of this series is: each term is the term two places before it with every letter moved back 8 places in the alphabet, wrapping past A round to Z.
The missing 5th term therefore comes from the 3rd term, FJUE, with each letter moved back 8:
Letter of FJUE | Position | Position − 8 | Letter of the missing term |
|---|---|---|---|
F | 6 | 6 − 8 = −2 → wraps to 24 | X |
J | 10 | 10 − 8 = 2 | B |
U | 21 | 21 − 8 = 13 | M |
E | 5 | 5 − 8 = −3 → wraps to 23 | W |
Reading the last column, the missing term is XBMW.
Cross-check. Now read the series through consecutive terms instead, and list the shift each letter takes at every step:
NRCH → IYNJ: −5, +7, +11, +2
IYNJ → FJUE: −3, +11, +7, −5
FJUE → AQFB: −5, +7, +11, −3
Steps 1 and 3 carry the same shift pattern in their first three letters (−5, +7, +11) while step 2 carries the other one (−3, +11, +7, −5), so the two patterns alternate and the step from AQFB to the missing term repeats step 2: A − 3 = X, Q + 11 = B, F + 7 = M, B − 5 = W. This second route lands on the same term, XBMW. In the fourth column alone the alternation does not close — steps 1 and 3 ought to match there but read +2 and −3 — and that single mismatch traces to the printed slip explained next; the shift used above, −5, is read directly off step 2 and is untouched by it.
Why the first term can look inconsistent. The fourth letter of the first term is the one place where neither reading closes: moving H back 8 gives Z, not the printed E, and step 1 ends in +2 where the alternating pattern wants −3. Both readings would close if the first term ended in M, so this one letter is a slip carried in the original paper itself and it is reproduced here exactly as printed. The main derivation never touches it: the back-8 rule is established by IYNJ → AQFB, where all four letters agree, and is then applied to FJUE. The cross-check reaches the same term once that one printed letter is set aside.