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Letter and symbol sums

Some reasoning papers replace numbers with letters or symbols. You work out the value of each one, do the calculation, then (often) turn the answer back into a letter. The maths is simple; the skill is keeping track.

What is tested

  • Substituting given values for letters
  • Finding a symbol's value from two short equations
  • Giving the answer in the form asked (a number or a letter)

Worked example

If A = 2, B = 5 and C = 10, what is C ÷ A + B? Give your answer as a letter.

  1. Replace the letters: 10 ÷ 2 + 5.
  2. Divide first: 10 ÷ 2 = 5.
  3. Then add: 5 + 5 = 10.
  4. Which letter is worth 10? C.

Answer: C

Exam-day checklist

  • Write the numbers under the letters before calculating.
  • Use the order of operations (× and ÷ before + and −).
  • Read whether the answer should be a number or a letter.
  • For symbol puzzles, solve the equation with only one unknown first.

Common mistakes

  • Answering with the number when a letter was asked for.
  • Working left to right when a division should come first.
  • Mixing up two symbols that look alike.

Try it yourself

1. ▲ + ▲ = 12 and ▲ + ● = 10. What is ●?

Show answer

4

Two triangles make 12, so ▲ = 6; then 6 + ● = 10 gives ● = 4.

2. If P = 3, Q = 4, R = 12 and S = 7, which letter equals P × Q?

Show answer

R

3 × 4 = 12, and R = 12.

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More topic guides

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