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compulsory · CSS study notes

3. Series, Pattern Completion and Coding-Decoding

CSS GSA — Paper 7, Part-II, Section VII, Sub-topic 3 (Series, Pattern Completion and Coding-Decoding)

Past Paper Weightage

  • High — number/letter series and coding-decoding are fast, formulaic questions that are easy marks once the shortcut is known.

Series/Pattern Completion — Shortcut Method

  • Step 1 (always first): Find the differences between consecutive terms. If they're constant — it's a simple arithmetic series (add a constant each time).
  • Step 2: If the differences aren't constant, find the differences of the differences (2nd-level differences). If THOSE are constant, the series follows a quadratic-type pattern (differences themselves form an arithmetic series).
  • Step 3: If differences don't help, check for a multiplicative pattern (each term × or ÷ a constant, i.e. geometric series), or check odd/even terms separately (some series alternate between two interleaved patterns).
  • For letter series: convert each letter to its alphabet position number (A=1, B=2, ... Z=26) and apply the same numeric-difference method, then convert back to a letter at the end.

Worked Example (Number Series)

  • Find the next number: 2, 6, 12, 20, 30, ___
    • Step 1: Differences: 6−2=4, 12−6=6, 20−12=8, 30−20=10 — not constant, but increasing by 2 each time.
    • Step 2: Since the differences themselves increase steadily (+2 each time), the next difference is 10+2=12.
    • Step 3: Next term = 30+12 = 42.

Worked Example (Letter Series)

  • Find the next letter: A, C, F, J, O, ___
    • Step 1: Convert to numbers: A=1, C=3, F=6, J=10, O=15.
    • Step 2: Find gaps: 3−1=2, 6−3=3, 10−6=4, 15−10=5 — gaps increase by 1 each time.
    • Step 3: Next gap = 6, so next position = 15+6 = 21, which is letter U.

Coding-Decoding — Shortcut Method

  • Step 1: Compare the original word to its code letter-by-letter (or position-by-position), and find the consistent shift/rule applied to EVERY letter (e.g., always +1, always +2, or a reversal).
  • Step 2: Once the rule is confirmed on the given example, apply the exact same rule to the new word asked about.
  • Common code types: simple forward/backward alphabet shift, reversing letter order, swapping specific letter pairs, or a number-substitution code (A=1, B=2...).

Worked Example (Coding)

  • If CAT is coded as DBU, how is DOG coded?
    • Step 1: Compare each letter: C→D (+1), A→B (+1), T→U (+1) — the rule is "shift every letter forward by 1."
    • Step 2: Apply to DOG: D→E, O→P, G→H.
    • Step 3: Answer: EPH.

MCQ Traps

  • Don't stop at the first-level differences if they aren't constant — always check second-level differences before assuming the series is "random"
  • In coding-decoding, verify your discovered rule against every letter of the example word before applying it — a rule that only fits 2 of 3 letters is wrong

Self-Test Questions

  1. Find the next number: 3, 7, 13, 21, 31, ___ (hint: check second-level differences)
  2. Find the next letter: Z, X, U, Q, L, ___ (hint: convert to numbers first)
  3. If BOOK is coded as CPPL, how is PAGE coded using the same rule?

Past-Paper MCQs (FPSC)

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The FPSC MCQ papers you shared (2024 and 2025) had no direct series or coding question.

Past-Paper Questions with Answers (FPSC)

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Every question below appeared in the FPSC papers you shared; the year and question number are in each title. Answers are worked out by me. The number-series questions (2018, 2021–2024) are answered in the Arithmetic and Geometric Sequences chapter.

  • CSS 2022 Q8(d): In a certain language BROTHER is written QDGSNQA. How is SISTER written? (5)
    1. Reverse BROTHER → REHTORB
    2. Shift each letter back by 1: R→Q, E→D, H→G, T→S, O→N, R→Q, B→A = QDGSNQA (matches the code)
    3. Apply to SISTER: reverse → RETSIS
    4. Shift back by 1: R→Q, E→D, T→S, S→R, I→H, S→R
    5. SISTER = QDSRHR
  • CSS 2017 Q8(D), 2019 Q7(d): COMPUTER is written RFUVQNPC. How is MEDICINE written? (5)
    1. Reverse COMPUTER → RETUPMOC
    2. Keep the first and last letters; shift every middle letter forward by 1: R, E→F, T→U, U→V, P→Q, M→N, O→P, C = RFUVQNPC (matches)
    3. Apply to MEDICINE: reverse → ENICIDEM
    4. Keep E and M at the ends; shift the middle: N→O, I→J, C→D, I→J, D→E, E→F
    5. MEDICINE = EOJDJEFM
    • The 2019 paper prints the code as FRUVQNPC, which looks like a typing error for RFUVQNPC
  • CSS 2018 Q8(D): LANDMINE is written PYRBQGRC. How is HOMEMADE written? (5)
    1. Compare letter by letter: L→P (+4), A→Y (−2), N→R (+4), D→B (−2), M→Q (+4), I→G (−2), N→R (+4), E→C (−2)
    2. The rule is +4, −2 alternately
    3. HOMEMADE: H+4 = L, O−2 = M, M+4 = Q, E−2 = C, M+4 = Q, A−2 = Y, D+4 = H, E−2 = C
    4. HOMEMADE = LMQCQYHC

CSS Exam Perspective

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  • Most repeated area: coding-decoding (2017, 2018, 2019, 2022): in a code, write the position shifts under each letter
  • Tip: first test a fixed shift, then alternating shifts, then reversal plus a shift