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Letter Series

Reasoning · Verbal Reasoning

7 Part4 worked examples17 practice questions

In a letter series a few English letters are written in a row, like B, E, H, K, ? — and you must say which letter replaces the question mark. The letters are not random; a hidden rule links them, and the same rule carries on.

The good news is that every letter series can be turned into a number series: A = 1, B = 2, … Z = 26. Once the letters are numbers, we know how to look at the gaps between numbers. This whole chapter is the extension of that one idea.

We start from zero: first the alphabet table and “going round the wheel”, then the easiest series (the same gap every time), then changing gaps, woven series and special numbers; after that series of groups of letters, and at the end filling blanks and catching a wrong letter.

How to use this chapter

  1. Read — the idea first, then the method.
  2. Study the solved example — at every step ask: why was this done?
  3. Try it yourself — write the places and gaps on paper, then choose an option. If stuck take the hint; open the solution last.
  4. Know the level — each question is marked Basic, Standard or Advanced.
NoteThe questions you get right are remembered in this browser. Check your progress in the panel on the right (the “Contents” button on a phone).
1

Foundation — the alphabet and how to read a series

Every question stands on these tools

The alphabet table, four steps to read a series and the simplest series (equal gaps).

The alphabet order and going round the wheel

The place of every letter from both ends

The places of the 26 letters, five landmarks, counting either way, A after Z and counting letters in between.

All letter-series questions run on the places of letters: A is first, B second … Z twenty-sixth. Under each letter there are two numbers — the upper one counts from A, the lower one from Z.

ABCDEFGHIJKLM
From A12345678910111213
From Z26252423222120191817161514
NOPQRSTUVWXYZ
From A14151617181920212223242526
From Z13121110987654321
The two places always add up to 27.

Without memorising the table

Remember five landmark letters: E = 5, J = 10, O = 15, T = 20, Y = 25. Every other letter is close to one. R is two steps before the landmark T (20), so 20 − 2 = 18.

After Z comes A — the wheel

Think of the alphabet as a wheel. If a place goes above 26, subtract 26; if it goes below 1, add 26. A series often runs past Z, and this is where mistakes often happen.

Opposite letters and letters in between

  • Opposite letters: the pairs A↔Z, B↔Y, C↔X … whose places add up to 27. M and N are opposites of each other.
  • Letters between two letters: bigger place − smaller place − 1 (the two ends are not counted).
Example 1 · Basic
Which letter is 3 places forward from O?
Solution, step by step
  1. 1O is at place 15. 15 + 3 = 18.
  2. 2The place is between 1 and 26, so there is no need to go round.
  3. 3The letter at place 18 is R.
Answer R
If you go above 26 or below 1, turn the wheel.
BasicTry it yourself first
Which letter is 12 places back from H?
BasicTry it yourself first
Which letter is 6 places back from I?
StandardTry it yourself first
Which letter is 6 places forward from O?
BasicTry it yourself first
What is the place of I in the English alphabet counted from the right (from Z)?
BasicTry it yourself first
Which letter is number 9 counted from the right end (from Z) of the alphabet?
StandardTry it yourself first
How many letters are there between H and K in the English alphabet?
StandardTry it yourself first
Which letter is the “opposite” of P (the A↔Z, B↔Y … pairing)?

Four steps to read a series

Letters → places → gaps → rule

The method of turning any letter series into numbers, looking at the gaps and recognising the rule from them.

Do not panic at a series. Run the same four steps every time:

Four steps
1. Write the place of each letter2. Write the gaps between neighbours (+/−)3. Recognise how the gaps behave4. Carry on the same behaviour

To help with step 3, the table below shows what the list of gaps looks like for each rule.

The list of gapsRuleExample
All equalSteady gapB D F H → +2, +2, +2
Two gaps in turnAlternating gapsA D F I K → +3, +2, +3, +2
Rising / falling by the same stepGrowing / shrinking gapsA B D G K → +1, +2, +3, +4
Messy, but equal every secondTwo woven seriesA Z B Y C X → +1 and −1 separately
Places square / prime / doublingSpecial numbersA D I P → 1, 4, 9, 16
NoteWhile writing the gaps always take right term − left term. Mind the + or − sign: a step back is negative.

Do not skip the check: the rule must fit every letter, not just the first two or three. Exam options are often built from a rule that fits the first few letters and then breaks.

Example 2 · Standard
Series: Q, O, R, P, S, Q, ? — which letter replaces the ?
Solution, step by step
  1. 1Write the place of each letter (A = 1 … Z = 26): Q O R P S Q → 17, 15, 18, 16, 19, 17.
  2. 2The gap from each letter to the next: −2, +3, −2, +3, −2.
  3. 3Rule: the gaps are −2, +3 in turn, and this pattern repeats.
  4. 4The next gap is +3. The letter just before the ? is Q (17); apply the gap to it: 17 + 3 = 20.
  5. 5The letter at place 20 is T.
Answer T
The list of gaps gave the rule away.
BasicTry it yourself first
Series: I, H, G, F, E, ? — which letter replaces the ?

Steady-gap series

The easiest type — the same step every time

Moving the same step forward or back every time, skipping letters, crossing Z and a blank inside the series.

The easiest letter series is one in which each letter is the same number of places ahead of (or behind) the one before. In B, D, F, H every step is +2 — skip one letter, take the next.

GapIn plain wordsExample
+1The very next letterC, D, E, F
+2Skip one letterB, D, F, H
+3Skip two lettersA, D, G, J
−2Skip one, going backwardsT, R, P, N
−3Skip two, going backwardsZ, W, T, Q

A long series can cross Z and start again from A. Take a +5 series: R, W, B, G, L — after W (23) comes 23 + 5 = 28, which is above 26, so 28 − 26 = 2, that is B.

TrickIf the ? is in the middle (like B, D, ?, H) the method is the same: take the gap between two known neighbouring letters (here B to D = +2) and apply it to the letter before the ?. Then run it on to the next letter to check.
Example 3 · Basic
Series: I, K, M, O, Q, ? — which letter replaces the ?
Solution, step by step
  1. 1Write the place of each letter (A = 1 … Z = 26): I K M O Q → 9, 11, 13, 15, 17.
  2. 2The gap from each letter to the next: +2, +2, +2, +2.
  3. 3Rule: each letter is 2 places ahead of the one before (+2).
  4. 4The next gap is +2. The letter just before the ? is Q (17); apply the gap to it: 17 + 2 = 19.
  5. 5The letter at place 19 is S.
Answer S
Check: the gap is the same in every pair.
Example 4 · Standard
Series: U, X, ?, D, G, J, M — which letter replaces the ?
Solution, step by step
  1. 1Write the place of each letter (A = 1 … Z = 26): U X D G J M → 21, 24, 4, 7, 10, 13.
  2. 2The gap from each letter to the next: +3, +3, +3, +3.
  3. 3Rule: each letter is 3 places ahead of the one before (+3).
  4. 4The next gap is +3. The letter just before the ? is X (24); apply the gap to it: 24 + 3 = 27; that is above 26, so subtract 26 → 1.
  5. 5The letter at place 1 is A. Check: the same rule carries on to the next letter.
Answer A
Do not forget to subtract 26 after crossing 26.
BasicTry it yourself first
Series: J, L, N, P, R, ? — which letter replaces the ?
BasicTry it yourself first
Series: H, I, J, K, L, ? — which letter replaces the ?
BasicTry it yourself first
Series: Z, W, T, Q, N, ? — which letter replaces the ?
BasicTry it yourself first
Series: Z, W, ?, Q, N, K, H — which letter replaces the ?
StandardTry it yourself first
Series: T, N, H, B, V, ? — which letter replaces the ?
StandardTry it yourself first
Series: Y, E, K, Q, W, ? — which letter replaces the ?
StandardTry it yourself first
Series: V, R, ?, J, F, B, X — which letter replaces the ?
AdvancedTry it yourself first
Series: Q, M, I, E, A, W, ? — which letter replaces the ?
AdvancedTry it yourself first
Series: U, P, ?, F, A, V, Q, L — which letter replaces the ?
2

Series with a changing pattern

Alternating, growing, woven and special numbers

When gaps are not equal: alternating gaps, growing or shrinking gaps, two woven series and special place numbers.

Alternating gaps

Two (or three) gaps repeating in a cycle

When gaps repeat as +a, +b, +a, +b…; it can also be seen as two series.

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Growing and shrinking gaps

+1, +2, +3, +4… or +7, +5, +3…

When the gaps themselves rise or fall by the same step; squares and triangular places are examples.

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Two woven series

Look at every second letter

When the letters come alternately from two separate series; the gaps look messy but are regular every second letter.

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Series of special numbers

Squares, primes and doubling numbers

When the places of the letters are square numbers, prime numbers or doubling; and the vowel series.

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3

Series of groups of letters

Several letters in each group — every column has its own series

Series of groups of two or three letters: reading column by column, pair rules and growing blocks.

A series of groups — column by column

The letters at each place form a series of their own

Solving a series of three-letter groups by splitting it into three separate series.

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Series of pairs

Opposite pairs and a fixed distance within a pair

Series of two-letter pairs: the link inside a pair and the gap from pair to pair.

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Growing and shrinking blocks

AB, ABC, ABCD… and the next letter in a long string

Series of blocks that gain (or lose) a letter each time, and the next letter in a long string written without gaps.

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4

Blanks and wrong letters

Repeating pieces and the broken rule

Filling blanks in a repeating pattern and catching a wrong letter or group in a series.

Blanks in a repeating series

Find the piece, fill the blanks

A series like ab_ca_bc in which a short piece repeats and some letters are blank.

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The wrong letter or group

Where the rule breaks

A series in which one letter (or group) is out of line and has to be caught.

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5

Strategy guide

Recognising the type and the common traps

The order of recognising the rule from the look of a series, and the common mistakes.

Spot it and solve it

The type from the look

The order in which to test the rules, judged from how the question looks.

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Common traps

The mistakes that keep happening

The commonest reasons for losing marks in letter series and how to avoid them.

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6

Mixed practice

All types mixed — first spot the type

All letter-series types in three levels.

Basic practice

One rule, a short series

Steady gaps, simple alternating, alphabet questions and a couple of easy groups.

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Standard practice

Changing patterns, woven series and groups

Alternating, growing gaps, woven series, special numbers, groups, blanks and wrong letters.

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Advanced practice

Long series, crossing Z, a three-gap cycle

Series crossing Z, a three-gap cycle, woven series, mixed columns, a long string and wrong groups.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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