Coding and decoding — SSC CGL Reasoning Notes

Concepts and rules

A coding question hides a fixed rule. You are shown one or more words with their codes, and you must find the rule and apply it to a new word, or decode a given code back into a word.

Alphabet positions: A=1, B=2, … , Z=26. Memorise the anchors E=5, J=10, O=15, T=20, Y=25 (the word EJOTY) so you can reach any letter in one or two steps.

Reverse position: counting from Z, a letter's reverse position is 27 − (its position). So Z=1, Y=2, A=26, and M (13) has reverse position 14.

Opposite letters: two letters are opposite when their positions add 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. Every letter has exactly one opposite and no letter is its own opposite.

Shift codes: each letter moves k places forward (+k) or backward (−k). The alphabet is circular, so Y+3 = B and C−4 = Y. Work with positions: add k, and if the result is above 26 subtract 26; if it is 0 or below add 26.

The shift need not be constant. Common patterns are +1, +2, +3, … (increasing), +2, −2, +2, … (alternating), or a shift equal to the letter's place in the word.

Rearrangement codes: the word may be written in reverse, split into halves that are each reversed, or have its first and last letters swapped, often combined with a shift.

Value codes: a word becomes a number such as the sum of its letter positions, sum of reverse positions, sum × a fixed number, sum + number of letters, or the product of first and last positions.

Letter-to-digit codes: each letter stands for one digit. Compare words that share letters; a letter common to two words must have the same digit in both codes.

A rule is accepted only if it reproduces every given example. If two rules fit one example, use the second example to separate them.

Method and shortcuts

Step 1: Compare lengths. Same length suggests a letter-by-letter rule; a number suggests a value code; the same letters in a different order suggest rearrangement.

Step 2: Write positions under the word and under the code, and write the difference (code − word) for each letter. A constant, increasing or alternating difference shows the shift at once.

Step 3: If the differences look random, check whether code letter + word letter = 27 (opposite) or whether the code matches the reversed word (compare the first code letter with the last word letter).

Step 4: For a number code, compute the position sum first; then test sum × k and sum + k against every example. With two examples, solve a × (sum) + b for a and b.

Shortcut: to decode, apply the inverse rule in reverse order. If the rule was 'reverse, then +1', decode by −1 and then reverse.

Shortcut: in options, check only the letter that differs between options. This fails if you have not first confirmed the rule on the given example.

Example 1: constant shift

Question: In a certain code language, MANGO is written as OCPIQ. How is APPLE written in that language?

Solution: M(13)→O(15), A(1)→C(3), N(14)→P(16), G(7)→I(9), O(15)→Q(17). Each letter moves +2. So A→C, P→R, P→R, L→N, E→G.

Answer: CRRNG.

Example 2: opposite letters

Question: If GOLD is coded as TLOW, how is SILVER coded?

Solution: G(7)+T(20)=27, O(15)+L(12)=27, L+O=27, D(4)+W(23)=27, so each letter is replaced by its opposite. S→H, I→R, L→O, V→E, E→V, R→I.

Answer: HROEVI.

Example 3: reverse and shift

Question: If TABLE is written as FMCBU, how is CHAIR written?

Solution: The code starts with F, which is E+1, and E is the last letter of TABLE. Reverse TABLE to ELBAT and add 1 to each letter: F M C B U, which matches. Reverse CHAIR to RIAHC and add 1: S J B I D.

Answer: SJBID.

Example 4: value code from positions

Question: In a code language, CAT = 27 and DOG = 29. What is the code for LION? (a) 50 (b) 52 (c) 54 (d) 58

Solution: CAT: 3+1+20 = 24, and 27 − 24 = 3 = number of letters. DOG: 4+15+7 = 26, and 29 − 26 = 3. Rule: position sum + number of letters. LION: 12+9+15+14 = 50, plus 4 letters = 54.

Note: with only 3-letter examples, 'sum + 3' also fits and would give 53, which is not an option, so the letter-count rule is the intended one. Option (a) 50 is the trap of forgetting the added part.

Answer: (c) 54.

Example 5: increasing shift

Question: In a certain code, FRIEND is written as HUMJTK. How is MOTHER written? (a) ORWMKY (b) OQXMKY (c) ORXLKY (d) ORXMKY

Solution: Differences: F(6)→H(8) +2, R(18)→U(21) +3, I(9)→M(13) +4, E(5)→J(10) +5, N(14)→T(20) +6, D(4)→K(11) +7. The shift starts at +2 and grows by 1.

MOTHER: M+2 = O, O+3 = R, T+4 = X, H+5 = M, E+6 = K, R+7 = Y. Each wrong option differs in exactly one letter, so check that letter only.

Answer: (d) ORXMKY.

Example 6: opposite letters with reversal

Question: If GARDEN is written as MVWIZT, how is FLOWER written? (a) UOLDVI (b) IVDLOU (c) IVDOLU (d) HVDLOU

Solution: The differences G→M and A→V are irregular, so test opposites. Opposites of GARDEN are T Z I W V M. The code MVWIZT is exactly this written backwards. Rule: replace each letter by its opposite, then reverse.

FLOWER → opposites U O L D V I → reversed I V D L O U. Option (a) forgets the reversal; (d) uses H, but the opposite of R is I.

Answer: (b) IVDLOU.

Common mistakes

Forgetting the wrap-around: X+4 is B. Subtract 26 when the position passes 26.

Confusing opposite letters with reversing the word. Opposite changes each letter (A→Z); reversing only changes the order.

Fixing the rule from the first letter only. In FRIEND→HUMJTK the first letter alone suggests +2 everywhere; always check all letters.

Counting positions wrongly in the middle of the alphabet. Use the anchors E=5, J=10, O=15, T=20 instead of counting from A.

In value codes, testing only the plain sum. If the sum misses by the same amount each time, look for an added constant or the number of letters.

Practice questions

Q1. If COLD is written as DQOH, how is WARM written? (a) XCUQ (b) XBUQ (c) YCUQ (d) XCVQ

Q2. In a code, ROSE = 6821, CHAIR = 73456 and PREACH = 961473. What is the code for SEARCH? (a) 214763 (b) 214673 (c) 241673 (d) 214637

Q3. In a code language, CAT = 48 and DOG = 52. What is the code for RAT? (a) 76 (b) 80 (c) 78 (d) 74

Answers

Q1. (a) Shifts are +1, +2, +3, +4: W+1 = X, A+2 = C, R+3 = U, M+4 = Q, giving XCUQ.

Q2. (b) From the words: R=6, O=8, S=2, E=1, C=7, H=3, A=4, I=5, P=9. SEARCH = S E A R C H = 2 1 4 6 7 3 = 214673.

Q3. (c) CAT sum 24 → 48 and DOG sum 26 → 52; a × 24 + b = 48 and a × 26 + b = 52 give a = 2, b = 0, so code = 2 × sum. RAT: 18+1+20 = 39, 2 × 39 = 78.

Quick revision

EJOTY: E=5, J=10, O=15, T=20, Y=25. Opposite letters add to 27; reverse position = 27 − position.

Write the difference under each letter: constant, increasing or alternating differences reveal shift codes.

If the first code letter is related to the last word letter, the word has been reversed.

Number codes: try sum, sum × k, sum + k, sum + letters; a rule must fit every example.

Concepts and rules

Word construction questions test whether you can build, rearrange or pick letters correctly. The main types are: which word can or cannot be formed, rearranging jumbled letters into a meaningful word, forming words from letters at given positions, counting letter pairs, and letter transformations.

Letter-count rule: each letter of the given word can be used only as many times as it appears. TERMINATE can come from DETERMINATION because that word has 2 T's and 2 E's; ROTATION cannot, because it needs 2 O's and there is only 1.

Order does not matter in 'can be formed' questions: the letters may be taken from anywhere in the given word.

A word fails for one of two reasons: a letter is missing altogether, or a letter is needed more times than it is available. Check missing letters first because that is faster.

Jumbled letters: rebuild the word using common endings and beginnings such as -ING, -TION, -ER, -LY, -NESS, UN-, RE-, and keep track of which letters remain.

Position-based formation: pick the letters at the stated positions, then count how many meaningful English words use all of them exactly once. Options are usually None, One, Two or More than two.

Letter pairs: count pairs of letters that have as many letters between them in the word as in the alphabet. A pair at word places i and j qualifies when j − i equals the difference of their alphabet positions. Count forward pairs (like S…T) and backward pairs (like U…T).

Transformations: a rule such as 'vowels → next letter, consonants → previous letter' is applied to the ORIGINAL letters, and only then are the new letters rearranged or counted.

The vowels are A, E, I, O, U. Y is treated as a consonant in these questions unless the question says otherwise.

Method and shortcuts

Step 1: Write the given word's letter counts, for example DETERMINATION: D1 E2 T2 R1 M1 I2 N2 A1 O1.

Step 2: For each option, first look for a letter absent from the table; then look only at letters that the option repeats.

Step 3: For letter pairs, take each letter in turn and compare it only with letters to its right; a pair that sits side by side in the word must be consecutive in the alphabet.

Shortcut: a pair can only qualify if its alphabet gap is smaller than the word length, so ignore far-apart letters like A and Z in a short word.

Shortcut: in 'how many meaningful words' questions, check the common anagram sets first (DIET/EDIT/TIDE/TIED, EARTH/HEART, LISTEN/SILENT) because the answer is often 'more than one'.

Example 1: which word cannot be formed

Question: Which word cannot be formed from the letters of CONVERSATION: REASON, SECTION or VACATION?

Solution: CONVERSATION has C1 O2 N2 V1 E1 R1 S1 A1 T1 I1. REASON and SECTION use each letter once and all are present. VACATION needs A twice, but there is only 1 A.

Answer: VACATION.

Example 2: rearranging jumbled letters

Question: The letters NIPCEL are rearranged to form a meaningful word. What is the last letter of that word?

Solution: The letters P, E, N, C, I, L form PENCIL, which uses each letter once.

Answer: L.

Example 3: counting letter pairs

Question: How many pairs of letters in COMPUTER have as many letters between them in the word as in the English alphabet?

Solution: Places in the word: C1 O2 M3 P4 U5 T6 E7 R8. M(13) and R(18): alphabet gap 5, word gap 8 − 3 = 5, valid. U(21) and T(20): gap 1 and side by side, valid. U(21) and R(18): gap 3, word gap 8 − 5 = 3, valid. T(20) and R(18): gap 2, word gap 8 − 6 = 2, valid. No other pair works.

Answer: 4 pairs (MR, UT, UR, TR).

Example 4: words from chosen positions

Question: How many meaningful English words can be made with the 3rd, 5th, 6th and 9th letters of PRESIDENT, using each letter once? (a) None (b) One (c) Two (d) More than two

Solution: P1 R2 E3 S4 I5 D6 E7 N8 T9, so the letters are E, I, D, T. Meaningful words: DIET, EDIT, TIDE and TIED, that is 4 words.

Answer: (d) More than two.

Example 5: repeated-letter trap

Question: Which word cannot be formed from the letters of ESTABLISHMENT? (a) THIMBLE (b) SMALLEST (c) TABLETS (d) MENTAL

Solution: ESTABLISHMENT has E2 S2 T2 A1 B1 L1 I1 H1 M1 N1. TABLETS needs T twice and S, E, A, B, L once each: available. THIMBLE and MENTAL use single letters that are all present. SMALLEST needs L twice, and there is only 1 L.

Answer: (b) SMALLEST.

Example 6: transform, arrange, locate

Question: In FOREIGN, each vowel is replaced by the next letter of the alphabet and each consonant by the previous letter. The new letters are then arranged in alphabetical order. Which letter is 3rd from the right? (a) J (b) M (c) P (d) F

Solution: F→E, O→P, R→Q, E→F, I→J, G→F, N→M, giving E P Q F J F M. Alphabetical order: E F F J M P Q. From the right: Q (1st), P (2nd), M (3rd).

Answer: (b) M.

Common mistakes

Checking only whether letters are present and ignoring how many times. Always compare counts for repeated letters such as LL, SS, OO.

Counting letter pairs in one direction only. U…R in COMPUTER is a backward pair and still counts.

Applying a transformation to letters that were already changed. Classify each letter as vowel or consonant using the original word.

Stopping after finding one meaningful word in position questions. Look for other anagrams before choosing 'One'.

Miscounting positions in long words. Write the place number under each letter before picking.

Practice questions

Q1. Which word cannot be formed from the letters of DETERMINATION? (a) MENTION (b) ROTATION (c) DORMANT (d) TERMINATE

Q2. How many pairs of letters in SHIPMENT have as many letters between them in the word as in the English alphabet? (a) 1 (b) 2 (c) 3 (d) 4

Q3. In MONITOR, each consonant is replaced by the next letter and each vowel by the previous letter. Which letter appears the most times in the new word? (a) O (b) H (c) N (d) S

Answers

Q1. (b) DETERMINATION has only 1 O, and ROTATION needs 2 O's. The other words fit the counts D1 E2 T2 R1 M1 I2 N2 A1 O1.

Q2. (c) S1 H2 I3 P4 M5 E6 N7 T8: S…P (alphabet gap 3, word gap 3), H…I (side by side), P…T (gap 4, word gap 4). 3 pairs.

Q3. (c) M→N, O→N, N→O, I→H, T→U, O→N, R→S gives N N O H U N S, in which N appears 3 times.

Quick revision

Make the letter-count table first; a word fails if a letter is missing or needed too many times.

A letter pair is valid when word gap = alphabet gap; count both directions.

Transform using the original letters, then arrange, then count places from the side asked.

For 'how many words', always check for more than one anagram.

Concepts and rules

Case-sensitive codes: when a question mixes capital and small letters, the case is part of the code. 'Pa' and 'pa' are different codes, just as 'Pa' and 'Po' are different.

Coded sentences: each word of a sentence has exactly one code, the same word always has the same code, and different words have different codes.

The order of codes need not follow the order of words. 'tea is hot' = 'Pa Ki ro' does not mean tea = Pa.

Common-word rule: if a word appears in two sentences, its code is among the codes common to both coded sentences. If exactly one word and exactly one code are common, they match.

Elimination rule: after fixing some words, the leftover words of a sentence take the leftover codes. If one word is left, its code is fixed; if two words share two leftover codes, neither code can be fixed.

A word that appears in only one sentence can still be decoded, but only after every other word in that sentence is fixed or grouped.

Letter-case rules: a rule may set case by type of letter (for example vowels become capitals, consonants become small) or by place (odd places capital, even places small). Classify each letter using the original word.

When a code cannot be fixed, the correct option is 'cannot be determined', and any option that names one of the possible codes is wrong because it is not certain.

Method and shortcuts

Step 1: Number the sentences and copy each coded sentence exactly, keeping capitals and small letters.

Step 2: Pick the word asked for, find every sentence containing it, and intersect their code sets. Remove codes already fixed for other words.

Step 3: If the word is in only one sentence, fix the other words of that sentence first through their own common sentences.

Step 4: For a case rule, write the original letter, its type (vowel or consonant) and its place, then the changed letter and its case, column by column.

Shortcut: scan options for case twins such as 'Ne' and 'ne'. The examiner usually places one as the trap, so match the case exactly.

Example 1: decoding by common words

Question: 'tea is hot' = 'Pa Ki ro', 'hot milk is good' = 'ro Su Ki nu', 'good tea' = 'nu Pa'. What is the code for 'milk'?

Solution: tea is in sentences 1 and 3, common code Pa, so tea = Pa. good is in sentences 2 and 3, common code nu, so good = nu. hot and is are in sentences 1 and 2, which share Ki and ro. In sentence 2, removing nu, Ki and ro leaves Su for milk.

Answer: Su. (The codes of hot and is cannot be separated.)

Example 2: a direct case rule

Question: In a code, each consonant is written as the same letter in small case and each vowel is replaced by the next letter in capital. CAT = cBt and DOG = dPg. How is RIVER written?

Solution: R consonant → r, I vowel → J, V consonant → v, E vowel → F, R → r.

Answer: rJvFr.

Example 3: the case trap

Question: 'Ram eats rice' = 'Lo mi Ta' and 'rice is cheap' = 'ta Mi Lo'. What is the code for 'rice'?

Solution: rice is the only common word. Ignoring case, mi/Mi, Ta/ta and Lo/Lo would all look common, but with case only Lo appears in both. So rice = Lo; Ram and eats share mi and Ta, and is and cheap share ta and Mi.

Answer: Lo.

Example 4: four coded sentences

Question: 'bright sun rises early' = 'Zo ka Ne pu', 'sun sets early today' = 'ka Ri pu Ze', 'today is bright' = 'Ze ne Zo', 'early rain today' = 'ka mo Ze'. What is the code for 'rises'? (a) Ne (b) ne (c) Zo (d) Ri

Solution: early is in sentences 1, 2 and 4: common code ka. today is in 2, 3 and 4: common code Ze. sun is in 1 and 2: common {ka, pu}, and removing ka gives pu. bright is in 1 and 3: common code Zo. Sentence 1 is now bright, sun, early = Zo, pu, ka, so rises = Ne.

Option (b) ne is the code of 'is' (the leftover in sentence 3), the case twin placed as a trap.

Answer: (a) Ne.

Example 5: fixed and unfixed codes

Question: 'Meena reads good books' = 'Ta Bu ko Ri', 'good books are costly' = 'Ri ta Bu Fe', 'Meena likes costly pens' = 'Fe Lo ko Ma'. What is the code for 'are'? (a) Ta (b) Fe (c) ta (d) Cannot be determined

Solution: good and books are common to sentences 1 and 2, whose common codes are Bu and Ri, so {good, books} = {Bu, Ri} in an unknown order. costly is common to 2 and 3: code Fe. Meena is common to 1 and 3: code ko.

Sentence 2 = good, books, are, costly = {Bu, Ri}, ?, Fe, so are = ta. Even though good and books cannot be separated, together they use up Bu and Ri, which is enough. Option (a) Ta is the code of 'reads'.

Answer: (c) ta.

Example 6: finding a case rule

Question: In a code, PLANET is written as sFmBko. How is MOTHER written? (a) qFgsPm (b) QfGSpL (c) qFgsPl (d) lPsgFq

Solution: The code starts with s, next to T, the last letter, so reverse first: T E N A L P. Compare: T→s (−1, small), E→F (+1, capital), N→m (−1, small), A→B (+1, capital), L→k, P→o. Rule: reverse; consonant −1 in small; vowel +1 in capital.

MOTHER reversed is R E H T O M → q F g s P l. Option (a) ends with m because it forgot to shift M; (d) is the code written in the wrong order.

Answer: (c) qFgsPl.

Common mistakes

Treating 'Mi' and 'mi' as the same code. Case is part of the code; read each letter's case before calling a code common.

Assuming codes follow word order. Always use common words, never places in the sentence.

Choosing one of two possible codes when two words share them. If the pair cannot be split, the answer is 'cannot be determined'.

Giving up on a word that appears only once. Fix the other words in its sentence and the leftover code belongs to it.

Deciding vowel or consonant from the shifted letter. In PLANET, E becomes F, but E still follows the vowel rule.

Practice questions

Q1. 'pen and ink' = 'Lu so Ga', 'ink is blue' = 'Ga mi Re', 'blue pen' = 'Re Lu'. What is the code for 'and'? (a) Lu (b) So (c) Ga (d) so

Q2. In a code, each vowel is replaced by the letter just before it, written in capital, and each consonant by the letter just after it, written in small. How is SOUP written? (a) tNTq (b) TntQ (c) tPVq (d) rNTo

Q3. 'sky is blue' = 'Ka Re pi', 'blue sea is deep' = 'pi So Re su', 'deep sky' = 'su Ka'. What is the code for 'sea'? (a) su (b) So (c) Su (d) Cannot be determined

Answers

Q1. (d) pen = Lu (sentences 1 and 3), ink = Ga (sentences 1 and 2), so and = so in small letters; 'So' does not occur at all.

Q2. (a) S → t (consonant, next, small), O → N (vowel, previous, capital), U → T, P → q: tNTq.

Q3. (b) sky = Ka (sentences 1 and 3), deep = su (sentences 2 and 3), {blue, is} = {Re, pi}, so sea = So. Su is a case trap.

Quick revision

Case is part of the code: Ne ≠ ne.

Common words ↔ common codes; never use word order.

Two words sharing two codes cannot be separated, but together they still remove those codes from the other words.

For case rules, classify each letter from the original word, then shift, then set the case.