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Series (Number & Letter)

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high importance~4 Q in Tier 16 formulas⚡ 10 shortcuts6 subtopics

Letters hide number series. Convert A=1 ... Z=26 (EJOTY: E=5, J=10, O=15, T=20, Y=25) and every letter series becomes a number series with wrap-around after Z.

Typical CGL letter rules:

  1. Constant step per letter: B, D, F, H (+2 each).
  2. Rising step: B, D, G, K, P (steps 2, 3, 4, 5).
  3. Alternating steps: A, C, B, D, C, E (steps +2, −1 repeating).
  4. Two-track clusters: in 'AZ, BY, CX' the first letters climb +1 while second letters fall −1.

Treat multi-letter clusters slot by slot — each letter-position is its own mini-series.

Detailed notes

Letters are numbers in disguise

Every letter series is a number series written in letters. Give each letter its place in the alphabet: A=1, B=2 ... Z=26. Now 'C, G, K, O' is just 3, 7, 11, 15 — add 4 each time. The next is 19 = S.

Learn the anchors: EJOTY

Counting from A every time is slow and causes mistakes. Remember five anchor letters:

EJOTY
510152025

Any letter is one or two steps from an anchor: M = O − 2 = 13, R = T − 2 = 18, W = Y − 2 = 23.

Also learn the reverse position (Z=1, Y=2 ... A=26). Rule: reverse position = 27 − position. The opposite pairs add up to 27: A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N.

Wrap-around

After Z the alphabet starts again at A. If a rule gives a number above 26, subtract 26: X(24) + 4 = 28 → 28 − 26 = 2 = B. Going backwards below A, add 26: C(3) − 5 = −2 → −2 + 26 = 24 = X.

Type 1: constant step

Every letter moves by the same number: C, G, K, O, S (+4). It can go backwards too: Z, W, T, Q (−3). It can cross Z: T, W, Z, C, F (+3).

Type 2: rising or falling step

The step itself changes: C, D, F, I, M (+1, +2, +3, +4, so next +5 → R). Or Y, W, T, P, K (−2, −3, −4, −5, so next −6 → E).

Type 3: two series mixed

Positions 1, 3, 5 form one series and positions 2, 4, 6 another: A, Z, C, X, E, V → A, C, E (+2) and Z, X, V (−2). Or the steps take turns: B, E, D, G, F, I (+3, −1, +3, −1).

Type 4: letter clusters

Each term is a group of 2-4 letters: BDF, GIK, LNP. Treat each position as its own series: first letters B, G, L (+5), second letters D, I, N (+5), third letters F, K, P (+5). Next: QSU. The slots can move in different directions: AZ, CX, EV (first letter +2, second letter −2).

Type 5: positions follow a number pattern

The positions themselves may be squares (A, D, I, P, Y = 1, 4, 9, 16, 25) or primes (B, C, E, G, K = 2, 3, 5, 7, 11).

Method in four steps

  1. Write the position number under every letter (use EJOTY).
  2. Find the number rule with the difference ladder.
  3. Apply it, using wrap-around if the result passes 26 or goes below 1.
  4. Convert back to a letter and match the option.

Quick revision

  • A=1 ... Z=26; anchors E5, J10, O15, T20, Y25.
  • Reverse position = 27 − position; opposite pairs add to 27.
  • Above 26 → subtract 26; below 1 → add 26.
  • Clusters: solve each slot separately.
  • Letters going forward and back → split into two series.
  • Squares (A, D, I, P, Y) and primes (B, C, E, G, K) are favourite hidden rules.

Types of questions asked

Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.

Type 1: Single letters with a constant step (forward, backward, wrap-around)very common3 practice Q
How to spot it:

Single letters that move the same distance each time, e.g. D, H, L, P.

Ln+1=Ln+k(mod26)L_{n+1} = L_n + k \pmod{26}
  1. Convert letters to positions (EJOTY anchors).
  2. Find the constant step.
  3. Add it; if the result passes 26, subtract 26 (below 1, add 26).

Why it works: a letter series is a number series in disguise.

Example: D, H, L, P, ?

Positions 4, 8, 12, 16 → +4. 16 + 4 = 20 = T.

Type 2: Rising or falling step between lettersvery common3 practice Q
How to spot it:

The gaps between letters grow (+1, +2, +3) or shrink by a fixed amount.

  1. Write positions and the step row.
  2. Continue the step row.
  3. Add the next step to the last letter.

Why it works: it is the letter version of the growing-difference number series.

Example: A, C, F, J, O, ?

Steps +2, +3, +4, +5 → next +6. O(15) + 6 = 21 = U.

Type 3: Two letter series mixed (alternate letters or alternating steps)common2 practice Q
How to spot it:

Letters jump forward and back, or the same two steps keep taking turns.

  1. Split odd places and even places, or write the step row.
  2. Solve each small series, or continue the step cycle.
  3. Pick the series that the '?' belongs to.

Why it works: two simple rules written one after the other look messy only when read together.

Example: B, Y, D, W, F, U, ?

Odd places B, D, F (+2) → next H. Even places Y, W, U (−2). The 7th term is an odd place → H.

Type 4: Letter-cluster series (each slot is its own series)very common3 practice Q
How to spot it:

Every term is a group of 2-4 letters, e.g. AC, EG, IK.

  1. Take the first letter of every cluster — find its rule.
  2. Do the same for the second letter, third letter ...
  3. Join the next letters of all slots.

Why it works: each slot moves by its own rule, often the same step, sometimes opposite directions.

Example: AC, EG, IK, ?

First letters A, E, I (+4) → M. Second letters C, G, K (+4) → O. Answer MO.

Type 5: Letter positions follow squares or primesoccasional2 practice Q
How to spot it:

The steps look irregular, but the positions are 1, 4, 9, 16 ... or 2, 3, 5, 7, 11 ...

  1. Write the positions of all letters.
  2. Check squares and primes directly on the positions.
  3. Take the next square or prime and convert it to a letter.

Why it works: the examiner hides a famous number list behind letters.

Example: C, E, G, K, M, ?

Positions 3, 5, 7, 11, 13 are primes. Next prime 17 = Q.

Formulas

Slot steps
si=Q(Li+1)−Q(Li)(mod26)s_i = Q(L_{i+1}) - Q(L_i) \pmod{26}

Steps per slot decide the rule; wrap Y→B counts as +3.

Two-track cluster
Q(firsti)=a+d1i,Q(secondi)=b+d2iQ(\text{first}_i) = a + d_1 i,\quad Q(\text{second}_i) = b + d_2 i

Tracks are independent; solve both.

Shortcut tricks

⚡ Step row under the letters

Write positions over the letters and steps between them. One clean step row (+2, +2, +2...) or a rising row (2, 3, 4, 5) ends the question.

Example: Q. B, D, G, K, ?

Sol. Steps: +2, +3, +4 → next +5. K(11) + 5 = P(16) → P.

Steps convert letters to arithmetic — never eyeball letter gaps.

⚡ Wrap-around fluency

After Z the alphabet restarts: Y + 4 = C. Practise from EJOTY anchors — every jump is at most 13, take the shorter direction.

Example: Q. X, Z, B, ?

Sol. X(24) +2 = Z(26), Z + 2 = B(2), B + 2 = D. The +2 step survives the wrap.

Wrap steps are the number one source of wrong letter answers — always add positions mod 26.

Where students lose marks

  • Counting backwards through Z incorrectly (Z − 2 is X, not 'nothing').

  • Missing rising steps: treating +2, +3, +4 as a flat '+3 average' gives a wrong letter.

  • Applying one track's step to both tracks of a cluster pair.

Practice sets — 17 questions

Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.

Topic test · 10 questions

Suggested time 5 min · wrong answers go to your mistake notebook automatically.