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Verbal Reasoning · Guide 7 of 8

Number codes and letter sums

Three question types where letters and numbers swap places: letter sums, missing numbers in brackets, and words written as number codes.

  • Ages 9 to 11
  • 11+ Verbal Reasoning
  • Worked examples

What is it?

Letter sums give each letter a number value. You swap the letters for their numbers, do the sum, then turn the answer back into a letter.

Missing number questions show three groups like 6 (18) 3. The number in brackets is made from the two outside numbers in the same way each time, and you find the missing one.

Number code questions write words as numbers, one digit for each letter. You match letters to digits, then code or decode another word.

A typical question

A = 2, B = 3, C = 5, D = 6, E = 10. What is B + C + A? Give your answer as a letter.

How to spot it

  • Letter sums: a list like A = 2, B = 3… followed by a sum using letters.
  • Missing numbers: three sets of numbers with one number in brackets, and a ? in the last set.
  • Number codes: words in capital letters with number codes such as 123 or 3214.

Step-by-step method

  1. Step 1: Letter sums: write the number under each letter before you calculate.
  2. Step 2: Follow BODMAS: brackets first, then × and ÷, then + and −.
  3. Step 3: Find the answer in the list and write the letter, not the number.
  4. Step 4: Missing numbers: try +, −, × and ÷ on the first set, then check the same rule works for the second set.
  5. Step 5: Number codes: find a letter that appears in two words (often the first or last letter) to lock in its digit.
  6. Step 6: Fill in a letter-to-digit table, then use it to code or decode the new word.

Worked examples

Example 1: a letter sum

Question: A = 2, B = 3, C = 5, D = 6, E = 10. What is (D × C) ÷ B? Give your answer as a letter.
  1. Step 1: Swap in the numbers: (6 × 5) ÷ 3.
  2. Step 2: Brackets first: 6 × 5 = 30. Then 30 ÷ 3 = 10.
  3. Step 3: 10 is E.

Answer: E

Example 2: missing number in brackets

Question: 4 (9) 5   6 (13) 7   8 ( ? ) 3
  1. Step 1: First set: 4 and 5 make 9. 4 + 5 = 9, so maybe the rule is 'add'.
  2. Step 2: Check the second set: 6 + 7 = 13. Yes.
  3. Step 3: Last set: 8 + 3 = 11.

Answer: 11

Example 3: a word code

Question: If TAP is written as 123 and PET as 341, what is the code for APT?
  1. Step 1: From TAP = 123: T = 1, A = 2, P = 3.
  2. Step 2: From PET = 341: P = 3 (matches), E = 4, T = 1 (matches).
  3. Step 3: APT: A = 2, P = 3, T = 1.

Answer: 231

Common traps

  • Leaving the answer as a number

    If the question asks for a letter, 10 is not an answer: E is.

  • Ignoring BODMAS

    A + B × C means multiply first. With A = 2, B = 3, C = 5 that's 2 + 15 = 17, not 25.

  • Checking only one set

    In missing number questions a rule that works once might be luck. It must work for both complete sets.

  • Mixing up codes and words

    In number code questions the codes may be in a different order from the words. Match them using repeated letters.

Top tips

  • Write neatly in columns: one letter, one number.
  • For missing numbers, common rules are add, multiply, take away, and 'double then add'.
  • Always check your final answer by putting it back into the question.

Practice questions

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