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Coding and Decoding for CUET General Aptitude

About 10 min to learn · 66 questions

A coding question hides one simple rule inside an example and asks you to use it on a new word. The whole skill is finding the rule quickly and checking it on every letter of the example before trusting it; almost every wrong option comes from a rule that fits the first two letters and fails on the third. This lesson covers letter positions, shift codes, reversals and opposites, decoding, letter-to-number codes, substitution codes and sentence codes, with worked examples and traps.

Syllabus area
Logical and Analytical Reasoning
On this page · 7 sections
  1. 01The core idea
  2. 02Letter codes
  3. 03Number, word and sentence codes
  4. 04Exam shortcuts
  5. 05Common mistakes
  6. 06Quick revision
  7. 07Check your understanding

The core idea

Find the rule from the example, test it on every letter of the example, and only then apply it. A rule that fits the first two letters but not the third is the source of almost every wrong option.

Letters are easiest as numbers. Know every position, A = 1 to Z = 26, and remember that opposite letters add to 27. Then a code is just a pattern in the gaps between numbers.

Letter codes

What is coding-decoding and how do you approach it?

Coding-decoding gives a word or sentence and its code, and asks you to code another word or decode a given code with the same rule. The main families are few.

FamilyWhat the example looks likeExample
Letter shiftEach letter moved forward or backTABLE → VCDNG
RearrangementThe same letters in a new orderSMILE → ELIMS
Opposite lettersA becomes Z, B becomes YCHAIR → XSZRI
Letters to numbersPositions, sums, productsWALL → 48
SubstitutionOne word stands for another"Chair is called table"
Sentence codesSentences and their coded forms"ta mo zi" = "we play chess"

What are the letter positions you must know by heart?

Every letter's position from A = 1 to Z = 26, and its reverse position, 27 minus the position. EJOTY gives landmarks at 5, 10, 15, 20 and 25: R is two before T, so 18; L is two after J, so 12.

ABCDEFGHIJKLM
12345678910111213
NOPQRSTUVWXYZ
14151617181920212223242526

Exam shortcut

The thirteen opposite pairs are A–Z, B–Y, C–X, D–W, E–V, F–U, G–T, H–S, I–R, J–Q, K–P, L–O and M–N. A few read as words or short forms: BY, GT, HS, IR, LO, MN.

How do you crack a letter-shift code?

Write the gap between each letter and its code letter, plus for forward and minus for back. If every gap is the same, it is a uniform shift; if the gaps follow a pattern, that pattern is the code.

Example 1 · A uniform shift

TABLE is coded as VCDNG. How is CHAIR coded?

  1. T to V, A to C, B to D, L to N, E to G: every letter moves two places forward.

  2. CHAIR: C to E, H to J, A to C, I to K, R to T.

Answer

EJCKT

PatternGapsExample
Uniform+2, +2, +2TABLE → VCDNG
Alternating+1, −1, +1, −1PAINT → QZJMU
Increasing+1, +2, +3, +4SMILE → TOLPJ
Decreasing−1, −2, −3, −4NOTE → MMQA

Example 2 · An increasing shift

In a code, each letter moves forward by its position in the word. How is SMILE coded?

  1. S + 1 = T, M + 2 = O, I + 3 = L.

  2. L + 4 = P, E + 5 = J.

Answer

TOLPJ

Watch out

The alphabet wraps round: two places forward from Y is A, and one back from A is Z. A code letter that seems to jump backwards, like A becoming Z in PAINT → QZJMU, is usually a wrap, not a new rule.

How can you tell a shift code from a reversal code?

Look at the letters before the gaps. If the code uses exactly the same letters as the word, it is a rearrangement; if it uses different letters, a shift or an opposite rule is involved.

  1. Same letters? Read the code backwards: SMILE → ELIMS is a reversal.
  2. Same letters, not reversed? Check pairs and halves: swapping pairs turns PLANET into LPNATE; reversing each half turns WINTER into NIWRET.
  3. Different letters, wild first gap? Compare the word's first letter with the code's last letter; a neat gap there means reversed and shifted.
  4. Random-looking gaps? Add the two positions; if each pair makes 27, it is an opposite-letter code.

Example 3 · Reverse and shift

PAPER is coded as QDOZO. How is the code built?

  1. P to Q is +1 but A to D is +3: no single shift.

  2. Reverse PAPER to get REPAP. REPAP to QDOZO: R to Q, E to D, P to O, A to Z, P to O. Every gap is −1.

Answer

Reverse the word, then move each letter back one place

With a uniform shift the order of the two steps does not matter. With increasing shifts it does, so test the rule on the full example.

Example 4 · Opposite letters

CHAIR is coded with opposite letters. What is the code?

  1. C 3 to X 24, H 8 to S 19, A to Z.

  2. I 9 to R 18, R 18 to I 9. Each pair adds to 27.

Answer

XSZRI

How do you decode a word instead of coding it?

Run the rule backwards: a code that moves letters forward by 3 is undone by moving back 3. Reversal, pair swaps and opposites undo themselves, but shifts do not: "+2 on odd places, −2 on even" is undone by "−2 on odd, +2 on even".

Watch out

The commonest slip is applying the rule a second time, which codes the code. Check by coding your decoded word again: you should get exactly the code in the question.

Number, word and sentence codes

How do letter-to-number codes work?

Each letter becomes a number, usually its position, its reverse position, or something built from them. Find which from the first letter, then confirm on the rest.

RuleCAT becomes
Positions3-1-20
Reverse positions, 27 − nn24-26-7
Position + 14-2-21
Double the position6-2-40
Sum of positions24
Product of positions60

Example 5 · A word's value

The value of a word is the sum of its letter positions. What is WALL?

  1. W = 23, A = 1, L = 12, L = 12.

  2. 23+1+12+12=4823 + 1 + 12 + 12 = 48.

Answer

48

Watch out

With one number for a whole word, many rules fit one example: "sum" and "sum plus 5" both do. Test on the second example if there is one. And split two-digit positions carefully: 192114 is 19, 21, 14, which is SUN.

How do you solve substitution codes?

In a substitution code each word is given another word's name. Decide what the real answer is first, then look up the name that real thing has been given.

Example 6 · Substitution

Chair is called table, table is called bed, bed is called sofa, and sofa is called stool. On what do people sleep?

  1. People really sleep on a bed.

  2. Bed is called sofa.

Answer

Sofa

The real word, bed, and the word called bed, table, are both waiting as wrong options.

Exam shortcut

Say it as "real thing, arrow, its new name". If the question gives a coded name, "she sat on a stool", read the list the other way: sofa is called stool. With swapped signs, replace every sign first, then use the usual order of operations.

How do you solve sentence codes by finding common words?

Put the sentences side by side and find a word that appears in two of them: the code shared by those two belongs to that word. Keep removing fixed words until the one you want stands alone. The codes are printed in jumbled order, so position tells you nothing.

Example 7 · Sentence codes

"ta mo zi" means "we play chess", "zi ku lo" means "they play cricket", and "lo ta fe" means "we watch cricket". What is the code for "chess"?

  1. "Play" is in sentences 1 and 2, which share "zi". "Cricket" is in 2 and 3, which share "lo". "We" is in 1 and 3, which share "ta".

  2. Sentence 1 minus "ta" and "zi" leaves "mo".

Answer

mo

Key idea

A word in no sentence gets a new code, unused anywhere. And two words that always appear together can never be separated, though you can remove them as a block: in "go home early" = "ra ne vi" and "home early today" = "vi ne tu", "go" is "ra" and "today" is "tu".

Exam shortcuts

  • Positions cold. EJOTY landmarks, opposites add to 27.
  • Same letters first. Same letters mean a rearrangement; different letters mean a shift or opposites.
  • Check every letter. The third letter separates most rules.
  • Decode backwards, then code again to check.
  • Common words fix sentence codes.

Common mistakes

  • Checking only the first letter or two.
  • Forgetting the wrap.
  • Reversing at the wrong moment with a non-uniform shift.
  • Coding the code when asked to decode.
  • 26 instead of 27 for opposites.
  • One example, many rules for number codes.
  • Splitting two-digit positions wrongly. 1 2 could be A, B or L.
  • Reading a substitution backwards.
  • Matching sentence codes by position.
  • Ignoring the order of operations after swapping signs.

Quick revision

Letters

  • A = 1 … Z = 26; reverse = 27 − position
  • EJOTY: 5, 10, 15, 20, 25
  • Opposites add to 27; wrap from Z to A

Shift or rearrange

  • Uniform, alternating, increasing, decreasing gaps
  • Same letters: reversal, pair swap, halves
  • Decode by undoing, then check

Other codes

  • Numbers: positions, reverse, sum, product
  • Substitution: real thing → its new name
  • Sentences: shared words, shared codes

The same position rules run through number and letter series and letter analogies.

Next · 06Quick revision

Check your understanding

66 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.

Letter-shift and reversal codesQ1 of 66Q1

Letter-shift and reversal codes

19 questions

Question 1

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In a certain code, MONDAY is written as NPOEBZ. How is FRIDAY written in that code?

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AnswerA · GSJEBZ

  1. Compare the two words letter by letter: M to N, O to P, N to O, D to E, A to B, Y to Z.

  2. Every letter has moved forward one place in the alphabet.

  3. Apply the same rule to FRIDAY: F becomes G, R becomes S, I becomes J, D becomes E, A becomes B, Y becomes Z.

  4. That gives GSJEBZ.

Worth noting

ESHCZX moves every letter backwards instead. Checking the last letter alone settles it: Y must become Z, not X.

Question 2

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In a certain code, PLANT is written as RNCPV. How is GRAIN written in that code?

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AnswerA · ITCKP

  1. Compare letter by letter: P to R, L to N, A to C, N to P, T to V. Each letter moves 2 places forward.

  2. Apply +2 to GRAIN: G to I, R to T, A to C, I to K, N to P.

  3. The code is ITCKP.

Worth noting

EPYGL moves every letter 2 places back instead of forward. ITBKP moves the A only one place.

Question 3

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If CLOUD is coded as BKNTC, what is the code for STORM?

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AnswerB · RSNQL

  1. C to B, L to K, O to N, U to T, D to C: every letter moves 1 place back.

  2. STORM: S to R, T to S, O to N, R to Q, M to L.

  3. The code is RSNQL.

Worth noting

TUPSN shifts forward. RSNQM leaves the last letter unchanged; check every letter, not only the first few.

Question 4

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In a code language, MANGO is written as OGNAM. How will PEARL be written in that language?

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AnswerC · LRAEP

  1. OGNAM is MANGO read from right to left, so the code simply reverses the word.

  2. PEARL read backwards is L, R, A, E, P.

  3. The code is LRAEP.

Worth noting

When the code uses exactly the same letters as the word, test reversal before trying any shift.

Question 5

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In a certain code, BIRD is written as YRIW. How is FISH written in that code?

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AnswerD · URHS

  1. B (2nd letter) became Y (25th), I (9th) became R (18th): each pair of positions adds up to 27, so every letter is replaced by its opposite letter.

  2. Opposites: F (6) to U (21), I (9) to R (18), S (19) to H (8), H (8) to S (19).

  3. The code is URHS.

Worth noting

A letter and its opposite always have positions adding to 27 (A–Z, B–Y, C–X …). URHT gets the last opposite wrong by one place.

Question 6

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If RIVER is written as ULYHU in a code, how is LAKE written in the same code?

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AnswerA · ODNH

  1. R to U, I to L, V to Y, E to H, R to U: each letter moves 3 places forward.

  2. LAKE: L to O, A to D, K to N, E to H.

  3. The code is ODNH.

Worth noting

NCMG uses a shift of 2, and IXHB a shift of 3 backwards. Fix the shift from one letter, then confirm it on a second.

Question 7

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In a certain code, BAKE is written as ZYIC. How is COOK written in that code?

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AnswerB · AMMI

  1. K to I and E to C show a shift of 2 places back. B to Z and A to Y agree once you wrap past A to the end of the alphabet.

  2. COOK: C to A, O to M, O to M, K to I.

  3. The code is AMMI.

Worth noting

Letters near the start wrap around: two places back from B is Z, and from A is Y. BNNJ uses a shift of only 1.

Question 8

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In a certain code, TIGER is written as SFHJU. How is HORSE written in that code?

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AnswerC · FTSPI

  1. Shifting TIGER does not give SFHJU directly, so reverse it first: REGIT.

  2. REGIT to SFHJU: R to S, E to F, G to H, I to J, T to U, a shift of +1.

  3. HORSE reversed is ESROH; +1 gives F, T, S, P, I.

  4. The code is FTSPI.

Worth noting

IPSTF shifts HORSE by +1 but forgets to reverse it. DRQNG reverses and then shifts the wrong way.

Question 9

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If FOREST is coded as GNSDTS, how is GARDEN coded?

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AnswerD · HZSCFM

  1. F to G is +1, O to N is −1, R to S is +1, E to D is −1, S to T is +1, T to S is −1.

  2. So the 1st, 3rd and 5th letters move forward 1 and the 2nd, 4th and 6th move back 1.

  3. GARDEN: G to H, A to Z (wrapping), R to S, D to C, E to F, N to M.

  4. The code is HZSCFM.

Worth noting

HBSEFO moves every letter forward. HZSCFO forgets the −1 on the last letter. Moving back from A wraps to Z.

Question 10

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In a code, CAMEL is written as DCPIQ. Using the same code, how is HOUSE written?

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AnswerA · IQXWJ

  1. C to D is +1, A to C is +2, M to P is +3, E to I is +4, L to Q is +5: each letter moves forward by its position in the word.

  2. HOUSE: H+1 = I, O+2 = Q, U+3 = X, S+4 = W, E+5 = J.

  3. The code is IQXWJ.

Worth noting

IPVTF uses +1 for every letter. GMROZ moves each letter BACK by its position. IQXVJ adds only 3 to S.

Question 11

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If BRIGHT is written as RBGITH in a certain code, how is STREAM written in that code?

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AnswerB · TSERMA

  1. Split BRIGHT into pairs: BR, IG, HT. The code RB, GI, TH swaps the two letters of each pair.

  2. STREAM in pairs: ST, RE, AM. Swapping each gives TS, ER, MA.

  3. The code is TSERMA.

Worth noting

MAERTS reverses the whole word, and EAMSTR swaps the two halves. Neither gives RBGITH from BRIGHT, so neither is the code.

Question 12

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In a certain code, PENCIL is written as NEPLIC. How is MARKET written in that code?

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AnswerC · RAMTEK

  1. Split PENCIL into halves PEN and CIL. NEP is PEN reversed and LIC is CIL reversed.

  2. MARKET splits into MAR and KET; reversing each half gives RAM and TEK.

  3. The code is RAMTEK.

Worth noting

TEKRAM reverses the whole word (that would turn PENCIL into LICNEP). RAMKET reverses only the first half.

Question 13

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In a code language, LION is written as ORLM. Which word is written as GRTVI in that language?

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AnswerD · TIGER

  1. L (12) became O (15) and I (9) became R (18): positions add to 27, so each letter is replaced by its opposite.

  2. The opposite code undoes itself, so decode GRTVI by taking opposites again.

  3. G to T, R to I, T to G, V to E, I to R.

  4. The word is TIGER.

Worth noting

IVTRG only reverses the code and HSUWJ shifts it forward by 1. The opposite rule works the same way in both directions.

Question 14

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If WATER is written as TXQBO in a code, which word is written as OXFK?

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AnswerA · RAIN

  1. W to T, A to X, T to Q, E to B, R to O: coding moves each letter 3 places back.

  2. To decode, move each letter of OXFK 3 places forward: O to R, X to A, F to I, K to N.

  3. The word is RAIN.

Worth noting

LUCH moves the code letters back again, which codes the code a second time instead of decoding it. To decode, run the rule backwards.

Question 15

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In a certain code, SPICE is written as WTMGI. How is SUGAR written in that code?

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AnswerB · WYKEV

  1. S to W, P to T, I to M, C to G, E to I: every letter moves 4 places forward.

  2. SUGAR: S to W, U to Y, G to K, A to E, R to V.

  3. The code is WYKEV.

Worth noting

VXJDU uses a shift of 3 and OQCWN shifts 4 places back. Count the shift from the example, don't guess it.

Question 16

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In a certain code, ZINC is written as XMRA. How is IRON written in that code?

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AnswerC · MLIR

  1. No single shift turns ZINC into XMRA. Reverse ZINC to get CNIZ.

  2. CNIZ to XMRA: C (3) to X (24), N (14) to M (13), I (9) to R (18), Z (26) to A (1). Each pair adds to 27, so these are opposite letters.

  3. IRON reversed is NORI; opposites of N, O, R, I are M, L, I, R.

  4. The code is MLIR.

Worth noting

RILM takes the opposites without reversing, and NORI reverses without taking opposites. Both steps are needed to turn ZINC into XMRA.

Question 17

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In a certain code, MOTHER is written as XJLWQN. How is SISTER written in that code?

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AnswerD · XJXVKT

  1. The code starts with X, which is R + 6, so read the code backwards: NQWLJX.

  2. M to N (+1), O to Q (+2), T to W (+3), H to L (+4), E to J (+5), R to X (+6): each letter moves forward by its position, and then the result is reversed.

  3. SISTER: S+1 = T, I+2 = K, S+3 = V, T+4 = X, E+5 = J, R+6 = X, giving TKVXJX.

  4. Reversed, the code is XJXVKT.

Worth noting

TKVXJX stops before the reversal. SGWWNY reverses the word first and then shifts, which does not turn MOTHER into XJLWQN.

Question 18

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If CANDLE is coded as BDEOFM, how is BASKET coded in the same way?

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AnswerA · BCLTUF

  1. Shift BDEOFM back by 1 to get ACDNEL.

  2. ACDNEL is CANDLE with each pair swapped: CA to AC, ND to DN, LE to EL.

  3. So the code swaps each pair and moves every letter 1 place forward.

  4. BASKET: pairs BA, SK, ET swap to AB, KS, TE, giving ABKSTE; +1 gives BCLTUF.

Worth noting

CBTLFU shifts without swapping. BCLTFU forgets to swap the last pair. ZAJRSD swaps correctly but shifts the wrong way.

Question 19

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In a code, SILVER is written as UGNTGP. Which word is written as DPKBIC in the same code?

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AnswerB · BRIDGE

  1. S to U is +2, I to G is −2, L to N is +2, V to T is −2, E to G is +2, R to P is −2.

  2. To decode, reverse each move: −2 on the 1st, 3rd and 5th letters, +2 on the 2nd, 4th and 6th.

  3. D to B, P to R, K to I, B to D, I to G, C to E.

  4. The word is BRIDGE.

Worth noting

FNMZKA applies the code again instead of undoing it. BNIZGA moves every letter back 2 and ignores the alternation.

Letters to numbers

17 questions

Question 20

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In a certain code, BEAD is written as 2514. How is FACE written in that code?

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AnswerB · 6135

  1. B, E, A, D are the 2nd, 5th, 1st and 4th letters of the alphabet, so each letter is replaced by its position.

  2. F = 6, A = 1, C = 3, E = 5.

  3. The code is 6135.

Worth noting

5316 writes the positions in reverse order, and 7246 adds 1 to each. BEAD keeps the letters in their own order.

Question 21

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In a code, HEN is written as 27. How is CUP written in that code?

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AnswerA · 40

  1. H = 8, E = 5, N = 14, and 8+5+14=278 + 5 + 14 = 27, so a word's code is the sum of its letter positions.

  2. CUP: C = 3, U = 21, P = 16.

  3. 3+21+16=403 + 21 + 16 = 40.

Worth noting

41 adds the reverse positions (24+6+11)(24 + 6 + 11), which would give HEN 54, not 27. 80 doubles the sum.

Question 22

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In a certain code, ACE is written as 26-24-22. How is BIG written in that code?

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AnswerC · 25-18-20

  1. A is written 26, C is written 24, E is written 22: letters are numbered from the end, Z = 1, Y = 2, …, A = 26.

  2. A letter's reverse position is 27 minus its position.

  3. B = 27−2=2527 - 2 = 25, I = 27−9=1827 - 9 = 18, G = 27−7=2027 - 7 = 20, so BIG is 25-18-20.

Worth noting

24-17-19 subtracts from 26 instead of 27. Check with A: 27−1=2627 - 1 = 26, which matches the example.

Question 23

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In a code, CAKE is written as 3-1-11-5. Which word is written as 7-1-9-14 in that code?

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AnswerD · GAIN

  1. C = 3, A = 1, K = 11, E = 5, so each number is the letter's position in the alphabet.

  2. Decode 7-1-9-14: 7 = G, 1 = A, 9 = I, 14 = N.

  3. The word is GAIN.

Worth noting

TZRM reads the numbers as reverse positions (Z = 1), which does not fit CAKE. GAIM reads 14 as M, but M is 13.

Question 24

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If FARM is coded as 38, what is the code for BOOK?

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AnswerB · 43

  1. FARM: 6+1+18+13=386 + 1 + 18 + 13 = 38, so the code is the sum of the letter positions.

  2. BOOK: B = 2, O = 15, O = 15, K = 11.

  3. 2+15+15+11=432 + 15 + 15 + 11 = 43.

Worth noting

41 takes O as 14. 47 adds the number of letters as well, which would make FARM 42.

Question 25

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In a certain code, HAND is written as 9-2-15-5. How is FOOT written in that code?

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AnswerA · 7-16-16-21

  1. H = 8, A = 1, N = 14, D = 4. The code numbers are one more: 9, 2, 15, 5.

  2. So each letter is written as its position plus 1.

  3. FOOT: 6+16 + 1, 15+115 + 1, 15+115 + 1, 20+120 + 1, giving 7-16-16-21.

Worth noting

6-15-15-20 is the plain positions; the example shows every number is one more than the position.

Question 26

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In a certain code, ANT is written as 46 and FLY is written as 38. How is BEE written in that code?

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AnswerD · 69

  1. The plain sums are ANT = 35 and FLY = 43, which do not match. Try reverse positions (Z = 1, …, A = 26).

  2. ANT: A = 26, N = 13, T = 7, total 46. FLY: F = 21, L = 15, Y = 2, total 38. Both fit.

  3. BEE: B = 25, E = 22, E = 22, total 69.

Worth noting

23 comes from 'sum + 11', which fits ANT but not FLY. Always test the rule on every example. 12 is the plain sum of BEE.

Question 27

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In a code, SKY is written as 165 and RAIN is written as 168. How is CLOUD written in that code?

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AnswerC · 275

  1. SKY: 19+11+25=5519 + 11 + 25 = 55, and 165=55×3165 = 55 \times 3. RAIN: 18+1+9+14=4218 + 1 + 9 + 14 = 42, and 168=42×4168 = 42 \times 4.

  2. So the code is the sum of the positions multiplied by the number of letters.

  3. CLOUD: 3+12+15+21+4=553 + 12 + 15 + 21 + 4 = 55, and 55×5=27555 \times 5 = 275.

Worth noting

220 multiplies by 4 (copied from RAIN) and 55 is the plain sum. The multiplier changes with the word's length.

Question 28

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If BED is written as 4-25-16 in a certain code, how is HAD written in that code?

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AnswerB · 64-1-16

  1. B = 2, E = 5, D = 4, and the code numbers are 4, 25, 16, which are 2², 5² and 4².

  2. So each letter is replaced by the square of its position.

  3. HAD: 82=648^2 = 64, 12=11^2 = 1, 42=164^2 = 16, giving 64-1-16.

Worth noting

16-2-8 doubles the positions instead of squaring them; for B = 2 both give 4, so check E: 5×2=105 \times 2 = 10, not 25. 64-2-16 wrongly squares 1 as 2.

Question 29

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In a certain code, CAR is written as 24-26-9. Which word is written as 7-12-15-23 in that code?

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AnswerC · TOLD

  1. C = 24, A = 26, R = 9: these are reverse positions (Z = 1, A = 26), found as 27 minus the position.

  2. To decode, subtract each number from 27: 27−7=2027 - 7 = 20, 27−12=1527 - 12 = 15, 27−15=1227 - 15 = 12, 27−23=427 - 23 = 4.

  3. 20, 15, 12, 4 are T, O, L, D. The word is TOLD.

Worth noting

GLOW reads the numbers as ordinary positions. It is a real word, which makes it tempting, but that reading would code CAR as 3-1-18.

Question 30

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In a code, SUN is written as 192114. How is MOON written in that code?

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AnswerB · 13151514

  1. S = 19, U = 21, N = 14; writing them side by side gives 192114.

  2. MOON: M = 13, O = 15, O = 15, N = 14.

  3. Side by side: 13151514.

Worth noting

14121213 uses reverse positions (M = 14, O = 12, N = 13). 14161615 adds 1 to every position.

Question 31

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In a certain code, LAMP is written as 16-13-1-12. How is DESK written in that code?

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AnswerD · 11-19-5-4

  1. L = 12, A = 1, M = 13, P = 16. The code 16-13-1-12 lists these from the last letter to the first.

  2. So the code reverses the word and writes each letter's position.

  3. DESK reversed is KSED: K = 11, S = 19, E = 5, D = 4, giving 11-19-5-4.

Worth noting

4-5-19-11 forgets to reverse. 16-8-22-23 uses reverse positions of KSED, a rule that would code LAMP as 11-14-26-15.

Question 32

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If ICE is written as 18-6-10, how is JAM written in the same code?

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AnswerA · 20-2-26

  1. I = 9, C = 3, E = 5, and the code numbers 18, 6, 10 are twice these.

  2. So each letter is written as double its position.

  3. JAM: 2×10=202 \times 10 = 20, 2×1=22 \times 1 = 2, 2×13=262 \times 13 = 26, giving 20-2-26.

Worth noting

12-3-15 adds 2 instead of doubling. For I that would give 11, not 18, so the example rules it out.

Question 33

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In a certain code, TREE is written as 56 and SUN is written as 60. How is PLANT written in that code?

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AnswerC · 73

  1. Plain sums: TREE = 20+18+5+5=4820 + 18 + 5 + 5 = 48 and SUN = 19+21+14=5419 + 21 + 14 = 54.

  2. The codes are 8 more and 6 more: TREE has 4 letters and SUN has 3, so the code adds 2 for each letter.

  3. PLANT: 16+12+1+14+20=6316 + 12 + 1 + 14 + 20 = 63; with 5 letters add 10, giving 73.

Worth noting

Adding a fixed 8 (from TREE alone) would make SUN 62, not 60, so the extra depends on the length. 63 is the plain sum.

Question 34

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In a code, BAG is written as 14 and ACE is written as 15. How is HID written in that code?

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AnswerD · 288

  1. The sums do not fit: BAG adds to 10, not 14. Try the product: B × A × G = 2×1×7=142 \times 1 \times 7 = 14.

  2. Check ACE: 1×3×5=151 \times 3 \times 5 = 15. The code is the product of the letter positions.

  3. HID: 8×9×4=2888 \times 9 \times 4 = 288.

Worth noting

21 is the sum 8+9+48 + 9 + 4. No sum rule fits both examples: BAG has the larger sum (10 against 9) but the smaller code. 72 forgets D.

Question 35

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In a certain code, HIDE is written as 9-11-7-9. How is LOAF written in that code?

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AnswerB · 13-17-4-10

  1. H = 8, I = 9, D = 4, E = 5, and the code numbers are 9, 11, 7, 9: 8+18 + 1, 9+29 + 2, 4+34 + 3, 5+45 + 4.

  2. So each position is increased by the letter's place in the word (1st letter +1, 2nd +2, 3rd +3 …).

  3. LOAF: 12+1=1312 + 1 = 13, 15+2=1715 + 2 = 17, 1+3=41 + 3 = 4, 6+4=106 + 4 = 10, giving 13-17-4-10.

Worth noting

13-16-2-7 adds 1 to every letter, which fits the H of HIDE but not the I (9+1=109 + 1 = 10, not 11). 14-19-7-14 adds twice the place.

Question 36

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In a code, CAR is written as 22 because 3+1+18=223 + 1 + 18 = 22. Which of these words gets the same code as LIME?

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AnswerC · DUCK

  1. The code of a word is the sum of its letter positions. LIME: 12+9+13+5=3912 + 9 + 13 + 5 = 39.

  2. DUCK: 4+21+3+11=394 + 21 + 3 + 11 = 39. FIRE: 6+9+18+5=386 + 9 + 18 + 5 = 38.

  3. HOLE: 8+15+12+5=408 + 15 + 12 + 5 = 40. SAND: 19+1+14+4=3819 + 1 + 14 + 4 = 38.

  4. Only DUCK also gives 39.

Worth noting

Words with no letters in common can share a sum-code. Add carefully: HOLE and FIRE miss by just one.

Substitution codes

14 questions

Question 37

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In a certain language, red is called blue, blue is called green, green is called yellow, yellow is called white and white is called black. In that language, what is the colour of a clear daytime sky?

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AnswerC · green

  1. A clear daytime sky is actually blue.

  2. In this language, blue is called green.

  3. So the answer is green.

Worth noting

Blue is the real colour, not its name in the language. Red is the colour that is CALLED blue, which answers a different question.

Question 38

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If pen is called book, book is called bag, bag is called desk and desk is called chair, in what does a student carry books to school?

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AnswerD · desk

  1. A student really carries books in a bag.

  2. Bag is called desk.

  3. So the answer is desk.

Worth noting

Book is the object that is CALLED bag, so it answers the reverse question. Find the real object first, then look up its new name.

Question 39

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In a code language, milk is called water, water is called juice, juice is called tea and tea is called coffee. In that language, what falls from the clouds as rain?

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AnswerA · juice

  1. Rain is water.

  2. Water is called juice in this language.

  3. So the answer is juice.

Worth noting

Milk is the drink that is CALLED water, which is the reverse question.

Question 40

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If eye is called hand, hand is called ear, ear is called leg, leg is called nose and nose is called mouth, with what does a person hear?

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AnswerB · leg

  1. A person hears with the ear.

  2. Ear is called leg.

  3. So the answer is leg.

Worth noting

Hand is the part that is CALLED ear. The question asks for the new name of the real ear.

Question 41

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In a certain language, cow is called goat, goat is called horse, horse is called camel and camel is called elephant. Which animal is known as the ship of the desert in that language?

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AnswerC · elephant

  1. The ship of the desert is the camel.

  2. Camel is called elephant.

  3. So the answer is elephant.

Worth noting

Horse is the animal that is CALLED camel, so choosing it answers the reverse question.

Question 42

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If train is called bus, bus is called aeroplane, aeroplane is called ship and ship is called car, which vehicle flies in the sky?

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AnswerD · ship

  1. The vehicle that really flies is the aeroplane.

  2. Aeroplane is called ship.

  3. So the answer is ship.

Worth noting

Bus is the vehicle that is CALLED aeroplane; the question asks what the aeroplane is called.

Question 43

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In a code language, teacher is called doctor, doctor is called lawyer, lawyer is called farmer and farmer is called engineer. In that language, who treats patients in a hospital?

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AnswerA · lawyer

  1. Patients are really treated by a doctor.

  2. In this language, doctor is called lawyer.

  3. So the answer is lawyer.

Worth noting

Doctor appears as a NAME in the list (it is the name of teacher), which pulls students towards teacher. Always start from the real person, then read across.

Question 44

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If spoon is called plate, plate is called knife, knife is called glass, glass is called bowl and bowl is called pan, what is used to cut vegetables?

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AnswerB · glass

  1. Vegetables are really cut with a knife.

  2. Knife is called glass.

  3. So the answer is glass.

Worth noting

Plate is what the list calls knife. Bowl is the name of glass, one step too far along the chain.

Question 45

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If P means '+', Q means '×', R means '−' and S means '÷', what is the value of 36 S 4 P 5 Q 3 R 8?

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AnswerA · 16

  1. Replace the letters: 36÷4+5×3−836 \div 4 + 5 \times 3 - 8.

  2. Division and multiplication first: 36÷4=936 \div 4 = 9 and 5×3=155 \times 3 = 15.

  3. Then 9+15−8=169 + 15 - 8 = 16.

Worth noting

34 works left to right, (9+5)×3−8(9 + 5) \times 3 - 8, ignoring the order of operations. 40 mixes up P and Q.

Question 46

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In a code language, pencil is called eraser, eraser is called sharpener, sharpener is called scale and scale is called compass. Asha says in that language, 'I drew a straight line along my compass.' What did she actually use?

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AnswerC · scale

  1. Here the question gives a NAME from the language and asks for the real object.

  2. Find which object is called compass: scale is called compass.

  3. So she used a scale, which is what one draws a straight line along.

Worth noting

Compass is only the name she used. Sharpener is the object that is CALLED scale, one step too far back along the list.

Question 47

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If rain is called wind, wind is called storm, storm is called cloud, cloud is called sun and sun is called fog, what gives us light during the day?

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AnswerD · fog

  1. Daylight really comes from the sun.

  2. Sun is called fog.

  3. So the answer is fog.

Worth noting

Cloud is the thing that is CALLED sun, so it is the tempting reverse answer.

Question 48

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In a certain code, sit means run, run means eat, eat means sleep and sleep means read. What does a hungry person want to do, in that code?

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AnswerA · sleep

  1. A hungry person really wants to eat.

  2. Eat means sleep in this code.

  3. So the answer is sleep.

Worth noting

Run is the word whose code is eat, so it answers the reverse question. Read is the code of sleep, a step too far.

Question 49

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If '+' means '÷', '−' means '×', '×' means '+' and '÷' means '−', what is the value of 18×4+2−5÷318 \times 4 + 2 - 5 \div 3?

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AnswerB · 25

  1. Replace every sign by what it means: × becomes +, + becomes ÷, − becomes ×, ÷ becomes −.

  2. The expression becomes 18+4÷2×5−318 + 4 \div 2 \times 5 - 3.

  3. Division and multiplication first: 4÷2=24 \div 2 = 2, then 2×5=102 \times 5 = 10.

  4. 18+10−3=2518 + 10 - 3 = 25.

Worth noting

52 works left to right, (18+4)÷2×5−3(18 + 4) \div 2 \times 5 - 3. 15.4 multiplies before dividing, 4÷(2×5)4 \div (2 \times 5); division and multiplication are done in order from left to right. 28 forgets the final − 3-\,3.

Question 50

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Which interchange of two signs makes the equation 18÷3×2+4−6=2818 \div 3 \times 2 + 4 - 6 = 28 correct?

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AnswerB · − and ×

  1. As written, the left side is 6×2+4−6=106 \times 2 + 4 - 6 = 10, not 28.

  2. Interchange − and ×: 18÷3−2+4×6=6−2+24=2818 \div 3 - 2 + 4 \times 6 = 6 - 2 + 24 = 28. This works.

  3. Check the others: + and − gives 12−4+6=1412 - 4 + 6 = 14; + and × gives 6+2×4−6=86 + 2 \times 4 - 6 = 8; × and ÷ gives 18×3÷2+4−6=2518 \times 3 \div 2 + 4 - 6 = 25.

  4. Only interchanging − and × gives 28.

Worth noting

Test each interchange with the order of operations: division and multiplication before addition and subtraction.

Sentence and word codes

16 questions

Question 51

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In a code language, 'pel zu kar' means 'sweet mango juice' and 'kar dim so' means 'cold juice please'. What is the code for 'juice'?

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AnswerA · kar

  1. 'juice' is the only word in both sentences.

  2. 'kar' is the only code in both.

  3. So 'juice' is 'kar'.

Worth noting

The codes may be in any order, so never match words to codes by position. Match what the sentences share.

Question 52

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In a certain code, 'nok bira tel' stands for 'birds fly high' and 'tel fam nok' stands for 'kites fly high'. Which code stands for 'kites'?

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AnswerB · fam

  1. 'fly high' is common to both sentences, and so are the codes 'nok' and 'tel'.

  2. Take those away from the second sentence: 'kites' is left, and so is 'fam'.

  3. So 'kites' is 'fam'.

Worth noting

'bira' is the leftover code of the FIRST sentence, so it is the code for 'birds'.

Question 53

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In a code language, 'la mi so' means 'red big ball', 'so ta ki' means 'ball is round' and 'ki mi pu' means 'big is good'. What is the code for 'big'?

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AnswerC · mi

  1. 'big' appears in the first and third sentences.

  2. The only code in both 'la mi so' and 'ki mi pu' is 'mi'.

  3. So 'big' is 'mi'.

Worth noting

'so' is shared by the first two sentences, so it is 'ball'. 'ki' is shared by the last two, so it is 'is'.

Question 54

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In a code, '4 7 9' means 'come here now' and '9 2 5' means 'now go home'. Which number stands for 'now'?

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AnswerD · 9

  1. 'now' is the only word in both sentences.

  2. 9 is the only number in both codes.

  3. So 'now' is 9.

Worth noting

4 and 7 belong to 'come' and 'here', but the sentences do not say which is which. Only the shared word is fixed.

Question 55

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In a code language, 'sa lo pin' means 'good morning friends' and 'pin ro sa' means 'good night friends'. What is the code for 'night'?

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AnswerD · ro

  1. 'good' and 'friends' are in both sentences, and so are 'sa' and 'pin'.

  2. The second sentence is left with 'night' and 'ro'.

  3. So 'night' is 'ro'.

Worth noting

'lo' is the leftover code of the first sentence, which is 'morning'. The code for 'good' cannot be told apart from 'friends'.

Question 56

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In a certain code, 'ja ko ri' means 'open the window', 'ri mu te' means 'close the door' and 'te ja ri' means 'open the door'. What is the code for 'window'?

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AnswerA · ko

  1. 'the' is in all three sentences; 'ri' is the only code in all three, so 'the' is 'ri'.

  2. 'open' is in the first and third sentences; apart from 'ri' they share 'ja', so 'open' is 'ja'.

  3. The first sentence 'ja ko ri' then leaves 'ko' for 'window'.

Worth noting

'te' is shared by the second and third sentences, so it is 'door'.

Question 57

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In a code language, 'bo fi ne' means 'tea is hot', 'ne ga lu' means 'coffee is cold' and 'lu fi da' means 'hot coffee sold'. Which word is coded as 'ga'?

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AnswerB · cold

  1. 'is' is in the first two sentences, and so is 'ne': 'is' is 'ne'.

  2. 'coffee' is in the last two, and so is 'lu': 'coffee' is 'lu'.

  3. The second sentence 'ne ga lu' leaves 'ga' for the word 'cold'.

Worth noting

'coffee' sits next to 'ga' in the second sentence, but the order of codes tells us nothing. 'coffee' is 'lu'.

Question 58

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In a certain code, 'tan ri vok' means 'children play football', 'vok mel si' means 'children read books', 'ri ja pet' means 'football is fun' and 'pet si nu' means 'books are fun'. Which pair of codes stands for 'play football'?

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AnswerC · tan ri

  1. 'children' is in the first two sentences: 'vok'. 'football' is in the first and third: 'ri'.

  2. The first sentence 'tan ri vok' then leaves 'tan' for 'play'.

  3. So 'play football' is 'tan ri'.

Worth noting

'vok ri' is 'children football' and 'ri pet' is 'football fun'. Fix each word separately before putting the pair together.

Question 59

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In a code language, 'dom kel sar' means 'clean fresh water', 'kel wu mi' means 'fresh fruit juice' and 'sar mi pla' means 'water and juice'. Which of these could be the code for 'clean air'?

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AnswerD · dom tez

  1. 'fresh' is in the first two sentences: 'kel'. 'water' is in the first and third: 'sar'.

  2. The first sentence then leaves 'dom' for 'clean'.

  3. 'air' appears in no sentence, so its code must be a code not used so far, such as 'tez'.

  4. So 'clean air' could be 'dom tez'.

Worth noting

'dom kel' uses 'kel', which is already the code for 'fresh'. A new word needs a new code.

Question 60

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In a certain code, '3 8 5' means 'sky is blue', '5 1 6' means 'blue sea water' and '6 8 2' means 'water is cool'. Which number is the code for 'sea'?

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AnswerA · 1

  1. 'blue' is in the first two sentences, so it is 5. 'water' is in the last two, so it is 6.

  2. The second sentence '5 1 6' then leaves 1 for 'sea'.

  3. So 'sea' is 1.

Worth noting

6 is 'water', shared by the second and third sentences. 3 and 2 are the leftover codes for 'sky' and 'cool'.

Question 61

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In a code language, 'mak to jil' means 'sun rises early', 'jil no fas' means 'early bird sings' and 'fas mak rep' means 'bird sees sun'. What is the code for 'sings'?

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AnswerA · no

  1. 'early' is in the first two sentences: 'jil'.

  2. 'bird' is in the last two: 'fas'.

  3. The second sentence 'jil no fas' leaves 'no' for 'sings'.

Worth noting

'rep' is the leftover code of the third sentence, which is 'sees'.

Question 62

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In a certain code, 'pi ga ter' means 'rivers flow down', 'nu vos li' means 'hills stand tall' and 'ter be nu' means 'rivers from hills'. What is the code for 'from'?

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AnswerB · be

  1. 'rivers' is in the first and third sentences: 'ter'.

  2. 'hills' is in the second and third: 'nu'.

  3. The third sentence 'ter be nu' leaves 'be' for 'from'.

Worth noting

The codes for 'flow' and 'down' cannot be separated ('pi' or 'ga'), and neither can 'stand' and 'tall'. That does not matter: 'from' is fixed.

Question 63

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In a code, '7 3 1' means 'please pass salt', '3 9 4' means 'pass the water' and '1 4 6' means 'salt and water'. Which number stands for 'the'?

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AnswerD · 9

  1. 'pass' is in the first two sentences: 3. 'water' is in the last two: 4.

  2. The second sentence '3 9 4' leaves 9 for 'the'.

  3. So 'the' is 9.

Worth noting

4 is 'water', not 'the'. 6 and 7 are the leftover codes of the third and first sentences ('and', 'please').

Question 64

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In a code language, 'ko lin pa tu' means 'buy fresh vegetables daily', 'tu ra ko' means 'fresh milk daily' and 'ra sem pa' means 'buy milk now'. What is the code for 'vegetables'?

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AnswerC · lin

  1. 'fresh' and 'daily' are both in the first two sentences, which share the codes 'ko' and 'tu'. We cannot tell which is which, but together they use up 'ko' and 'tu'.

  2. 'buy' is in the first and third sentences, which share only 'pa'.

  3. In 'ko lin pa tu', removing 'ko', 'tu' and 'pa' leaves 'lin' for 'vegetables'.

Worth noting

A pair of words that always appear together can never be separated, but you can still remove them as a block.

Question 65

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In a certain code, 'lo mi pak' means 'green tea helps', 'mi pak sur' means 'tea helps sleep', 'sur ka bin' means 'sleep well early' and 'bin dos fu' means 'early morning walk'. For which word can the code NOT be found?

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AnswerD · tea

  1. 'tea' and 'helps' appear together in the first two sentences and nowhere else, so they share 'mi' and 'pak' with no way to split them.

  2. 'green' is what is left of the first sentence after 'mi' and 'pak': 'lo'. 'sleep' is in the second and third sentences: 'sur'.

  3. 'early' is in the third and fourth: 'bin'. The third sentence then leaves 'ka' for 'well'.

  4. So only the code for 'tea' cannot be found.

Worth noting

Two words that always appear together can never be told apart. 'green' looks harder because it appears once, but elimination fixes it.

Question 66

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In a code language, 'ruk pim tas' means 'students love science', 'tas lo vim' means 'science needs patience', 'vim del kor' means 'patience brings success' and 'kor ruk yen sa' means 'success makes students happy'. What is the code for 'love'?

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AnswerA · pim

  1. 'science' is in the first two sentences: 'tas'.

  2. 'students' is in the first and fourth sentences, and the only code they share is 'ruk'.

  3. The first sentence 'ruk pim tas' then leaves 'pim' for 'love'.

Worth noting

'yen' belongs to 'makes' or 'happy', which cannot be separated. Use only the sentences you need.

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