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IMAT Logical Reasoning · Spatial and Sequence Reasoning

Letter Sequences and Letter Codes

Turn each letter into its position in the alphabet, and a letter sequence or code becomes a number problem.

All Spatial and Sequence Reasoning notes

Why this matters

No past IMAT paper has asked a letter sequence yet. They test the same skill as number sequences and are standard in reasoning tests, so the method is worth the few minutes it takes to learn.

Concept 1 of 2: Alphabet positions and letter sequences

Letters are numbers in disguise: A is 1 and Z is 26. Convert, find the number rule, then convert back. A few anchor letters make the conversion fast: E is 5, J is 10, O is 15, T is 20, Y is 25.

Definition

  • Position: A = 1, B = 2, …, Z = 26. Anchors: E 5, J 10, O 15, T 20, Y 25.
  • Position from the end: Z is 1st from the end, A is 26th. Position from the end = 27 minus the position.
  • Wrap-around: after Z comes A again. Subtract 26 from any position above 26.
  • Pairs of letters may move in opposite directions, for example AZ, BY, CX, where each pair adds to 27.
LettersPositionsPositions from the end
A B C D E1 2 3 4 526 25 24 23 22
F G H I J6 7 8 9 1021 20 19 18 17
K L M N O11 12 13 14 1516 15 14 13 12
P Q R S T16 17 18 19 2011 10 9 8 7
U V W X Y21 22 23 24 256 5 4 3 2
Z261
Learn the anchors E, J, O, T, Y and count from the nearest one.
Practice this conceptself-check · 4 quick reps

Position from the end is 27 minus the position

Z is 1st from the end, not 0th. So a letter at position pp is 27−p27 - p from the end: M (13) is 14th from the end. Using 26 minus the position puts you one letter off, and that letter is usually an option.

Concept 2 of 2: Letter codes: shifts and reversed alphabets

In a simple code every letter is moved the same number of places along the alphabet. Compare one original letter with its coded letter to find the shift, check it on a second letter, then apply it to the new word.

Definition

  • A shift code moves every letter kk places forward (or back), wrapping from Z to A.
  • Find kk from one letter pair, then check it on every letter of the example: codes sometimes use different shifts for different positions.
  • A reversed alphabet code swaps A with Z, B with Y, and so on: each pair of positions adds to 27.
  • To decode, apply the shift in the opposite direction.

Shift code

coded position=position+k(subtract 26 if above 26)\text{coded position} = \text{position} + k \quad (\text{subtract } 26 \text{ if above } 26)
  • kkthe shift; negative means move backwards

Worked example

With a shift of 3, how is CAT coded? With the same code, which word is coded as JRR?
Practice this conceptself-check · 3 quick reps

Shifts wrap from Z back to A

With a shift of +3, X becomes A, not a symbol beyond Z. Forgetting to subtract 26 gives a position like 27, and an option that skips the wrap is often there to catch it.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

  • Letter codes: shifts and reversed alphabets

    Shift code

    coded position=position+k(subtract 26 if above 26)\text{coded position} = \text{position} + k \quad (\text{subtract } 26 \text{ if above } 26)

Reference tables (1)

Alphabet positions and letter sequences6 rows
LettersPositionsPositions from the end
A B C D E1 2 3 4 526 25 24 23 22
F G H I J6 7 8 9 1021 20 19 18 17
K L M N O11 12 13 14 1516 15 14 13 12
P Q R S T16 17 18 19 2011 10 9 8 7
U V W X Y21 22 23 24 256 5 4 3 2
Z261
Learn the anchors E, J, O, T, Y and count from the nearest one.

Watch out for (2)

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