Coding and Decoding notes

MDCAT Analytical and Logical Reasoning

Coding and decoding questions use a hidden rule to change letters, words, numbers, mathematical signs or artificial-language terms. To solve them, identify the exact transformation from the example, apply it in the same order, and check alphabet wraparound when necessary.

Meaning and Basic Method of Coding and Decoding

Coding means changing a word, letter, number or sign according to a fixed rule. Decoding means finding the original form or applying the reverse rule. In reasoning questions, the rule is usually shown through one or more examples.

Start by comparing each original letter with its coded letter. Check whether the change is a fixed shift, reversal, rearrangement, position-based change, numerical operation or a combination of rules. Apply the steps in the stated order.

Alphabet positions are A = 1, B = 2, C = 3, up to Z = 26.
CAT to DBU uses a shift of one place forward for every letter: C to D, A to B, T to U.
DOG coded by the same rule is EPH: D to E, O to P, G to H.
MADRAS to NBESBT also uses one place forward for every letter.
BOMBAY therefore becomes CPNCBZ.
When a question gives a complete rule, use the rule directly instead of trying to find another pattern.
Always preserve the number of letters unless the question specifically asks for a numerical code.

Alphabet Shifts and Wraparound

In a shift code, every letter moves a fixed number of places forward or backward. A forward shift of three changes A to D and M to P. A backward shift of two changes F to D.

Alphabet wraparound means continuing from the beginning after Z or from the end before A. For example, shifting Z one place forward gives A. Shifting B three places backward gives Y.

EARTH shifted three places forward becomes HDUWK: E to H, A to D, R to U, T to W, H to K.
MOTHER to PRWKHU shows a forward shift of three places.
A forward shift of one changes Z to A.
A backward shift of one changes A to Z.
For a shift of n, add n to the alphabet position and subtract 26 if the result is greater than 26.
For a backward shift, subtract n and add 26 if the result is less than 1.
Use the same shift separately on every letter.

Reversal and Rearrangement Codes

Some codes do not change the letters themselves. They only change their order. The most direct example is complete reversal. Other questions divide letters into odd and even positions, move the first letter to the end, or use a combination of rearrangement and shifts.

Number positions from left to right, beginning with 1. In TRAIN, the odd-position letters are T, A and N, while the even-position letters are R and I.

Complete reversal: STAR becomes RATS, so MANGO becomes OGNAM.
Moving the first letter to the end: TEAM becomes EAMT, so ROAD becomes OADR.
Odd-position letters followed by even-position letters: TRAIN becomes TANRI before any further shift.
For FISH, odd positions give F and S, and even positions give I and H. The rearranged form is FSIH.
If letters are rearranged and shifted, complete the rearrangement before applying the shifts.
Position numbers are counted in the original word unless the question states otherwise.
Reversal changes order but does not change the identity of any letter.

Position-Based Letter Operations

A position-based code gives a different operation to each letter according to its location in the word. The letter value may be multiplied by its position, shifted by its position, or changed according to whether its position is odd or even.

For multiplication codes, convert the result back into a letter. If the result is greater than 26, use alphabet wraparound. This is equivalent to repeatedly subtracting 26 until the answer is between 1 and 26.

For CODE, multiply each letter value by its position: C times 1 = 3, O times 2 = 30, D times 3 = 12, E times 4 = 20.
Using wraparound, 30 becomes 4, or D. The letters are C, D, L, T, and reversal gives TLDC.
For MATE, the products are M times 1 = 13, A times 2 = 2, T times 3 = 60, and E times 4 = 20.
The coded letters are M, B, H, T. Reversing them gives THBM.
Odd and even positions may follow different rules. Read the wording carefully before changing any letter.
In FISH, odd-position letters stay unchanged and even-position letters move one place backward. The result is FHSG.
FISH under the rule that each consonant moves to the next consonant while vowels stay unchanged becomes GITJ.

Vowel and Consonant Codes

Some questions treat vowels and consonants separately. A vowel cycle may be given, so the next vowel after U is A. In another type, vowels remain unchanged while only consonants move.

Do not treat the vowel cycle as the ordinary alphabet. The cycle A, E, I, O, U, A has five positions and returns to A after U.

Vowel cycle: A changes to E, E to I, I to O, O to U, and U to A.
MATE becomes METI under this cycle: A to E and E to I, while M and T remain unchanged.
CODE becomes CUDI: O to U and E to I, while C and D remain unchanged.
If vowels stay unchanged and consonants move to the next consonant, FISH becomes GITJ.
In FISH, F to G, I stays I, S to T, and H to J because the next consonant after H is J.
The next consonant means the next letter that is a consonant, not necessarily the next alphabet letter.
Always identify whether the rule concerns vowels, consonants, or both groups.

Number Codes Based on Letter Values

A word may be converted into a number by using alphabet positions. The question may ask for the total of all letters, a combination involving word length, or only the first and last letters. Write the formula before calculating.

For a first-and-last-letter code, ignore all middle letters. For a formula involving the word length, calculate the letter total first, then apply multiplication or addition in the stated order.

The alphabet value of a letter is its position: A = 1, B = 2, C = 3, and Z = 26.
Code formula 1: add all letter values, multiply by word length, then add the first-letter value.
CODE has total 3 + 15 + 4 + 5 = 27. Its code is 27 times 4 plus 3 = 111.
MATE has total 13 + 1 + 20 + 5 = 39. Its code is 39 times 4 plus 13 = 169.
Code formula 2: add the values of the first and last letters only.
CAGE has code 8 because C + E = 3 + 5 = 8.
MINT has code 33 because M + T = 13 + 20 = 33.

Numerical Writing and Digital Reduction

In direct numerical coding, each letter is replaced by its alphabet position. The positions may be separated by hyphens or written as a continuous string with fixed-width two-digit values.

Digital reduction means repeatedly adding the digits of a number until only one digit remains. The word may first be reversed, so the order of operations matters.

BOOK becomes 2-15-15-11 because B = 2, O = 15, O = 15 and K = 11.
CAP becomes 3-1-16.
For two-digit writing, use a leading zero for positions 1 to 9. Thus C is 03, D is 04 and E is 05.
Reverse the digits of each two-digit value separately. CODE becomes 30 51 40 50, written as 30514050.
In the digital-reduction code, first reverse the word, then replace letters by positions, then reduce each number.
FISH reversed is HSIF. H = 8, S = 19, I = 9 and F = 6.
The reduced values are 8, 1, 9 and 6, so FISH is coded as 8196.

Alternating Shifts and Combined Rules

Some questions combine two or more operations. The order is essential. A word may first be reversed, then its letters may be shifted by alternating amounts. Another rule may add the word length to each letter and then reverse the result.

Write every intermediate form. This prevents applying a correct operation in the wrong order.

For TRAIN, reverse first: TRAIN becomes NIART.
Apply shifts of plus 2, minus 3, plus 4, minus 5 and plus 6 to NIART.
The results are P, F, E, M and Z, so TRAIN becomes PFEMZ.
Adding the word length to every letter means adding the same number to each alphabet position.
For LAMP, the length is 4. Adding 4 gives P E Q T, and reversing gives TQEP.
For TRAIN, add 5 to each letter: Y W F N S. Reversal gives SNFWY.
Use alphabet wraparound in every combined rule whenever a shift crosses Z.

Symbol Substitution and Artificial Languages

In symbol-substitution questions, mathematical signs are given new meanings. Replace every sign first, then solve the resulting equation using the ordinary order of operations. The displayed symbol and its new meaning must not be confused.

Artificial-language questions use common parts of translated words. A part shared by two translated terms usually represents the shared meaning. The remaining part represents the remaining meaning.

If minus means plus, plus means minus, multiplication means division, and division means multiplication, replace all signs before calculating.
For 30 * 5 - 4 + 10 + 15, the replaced equation is 30 divided by 5 plus 4 minus 10 minus 15, which equals negative 15.
For 30 * 5 - 4 + 10 - 30, the replaced equation is 30 divided by 5 plus 4 minus 10 plus 30, which equals 30.
In the artificial language, dionot means oak tree and blyonot means oak leaf. The common part onot means oak.
Blycrin means maple leaf. Since bly means leaf, crin means maple.
A word that could mean maple syrup is crinweel, where crin means maple and weel means syrup.
Use word parts only when the examples support the shared meaning. Do not assume that an unmatched part has a meaning without evidence.

Key terms

Coding: Changing letters, words, numbers or signs according to a fixed rule.
Decoding: Finding the original form or applying the reverse of a coding rule.
Alphabet position: The numerical place of a letter, with A = 1 and Z = 26.
Forward shift: Moving a letter toward Z by a stated number of alphabet places.
Backward shift: Moving a letter toward A by a stated number of alphabet places.
Alphabet wraparound: Continuing from A after Z or from Z before A during a shift.
Reversal: Writing the letters of a word in the opposite order.
Odd position: A position such as 1, 3 or 5 when letters are counted from the left.
Even position: A position such as 2, 4 or 6 when letters are counted from the left.
Vowel cycle: The repeated sequence A, E, I, O, U, A used for vowel changes.
Consonant shift: Replacing a consonant with another consonant according to a stated order.
Word length: The total number of letters in a word.
Digital reduction: Repeatedly adding the digits of a number until one digit remains.
Symbol substitution: Giving mathematical signs meanings different from their usual meanings.
Artificial language: A constructed language in which word parts are inferred from translations.

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Analytical and Logical Reasoning shortcuts

Choosing the stronger supporting argument

Choose the option that directly explains why the claim is true. Prefer relevant evidence with a clear link to the claim, not a statement that is merely related.

Identify the claim and ask, “Why would this make the claim true?”
Reject personal opinions, unrelated facts and extreme statements.
Example: “Teachers should be paid more” is supported by “They shape future generations.”

This shortcut does not apply when the option gives direct statistical or experimental evidence that is stronger than a general reason.

Finding the pattern in letter and number series

Check letters and numbers separately. Look for equal increases, alternating changes, multiplication, or a repeating pattern.

Convert letters to positions if needed, such as A = 1 and D = 4.
Find the change in the letters and in the numbers independently.
Example: A2, D4, G6, J8 has letters increasing by 3 and numbers by 2, so the answer is M10.

Do not assume a simple addition pattern if alternating or multiplication patterns fit all the given terms.

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