11+ Verbal reasoning · Topic explained
Letter sums and logic problems
If A = 10 and B = 2, which letter is A + B?
The big idea
Swap letters for numbers, work it out, then swap back to a letter. In logic puzzles, line the facts up in order.
Picture it
Like lining up for a photo by height: put each fact in its place and the answer stands out.
Key words
- value
- the number a letter stands for
- letter answer
- turn your number back into a letter at the end
- times first
- do times and divide before add and take away
- must be true
- true for sure from the facts, not just possibly true
Worked examples
- 1Warm-up
A = 10, B = 2, C = 12, D = 11, E = 8. What is A + B, as a letter?
- A + B = 10 + 2 = 12
- 12 is C.
- 211+ standard
A = 9, B = 6, C = 7, D = 30, E = 4. What is E × A − B, as a letter?
- E × A = 4 × 9 = 36
- 36 − B = 36 − 6 = 30
- 30 is D.
- 311+ standard
Ben is younger than Zara and Nina. Raj is older than Nina. Max is older than Raj. Who is the youngest?
- Line them up: Max, Raj, Nina… then Ben below Nina.
- Zara is older than Ben too.
- The youngest is Ben.
- 411+ standard
Omar is faster than Yusuf and Harry. Priya is slower than Yusuf. Which must be true? (a) Harry is slowest (b) Omar is faster than Priya (c) Yusuf is faster than Harry
- Omar → Yusuf → Priya: so Omar is faster than Priya.
- We don't know where Harry fits next to Yusuf or Priya.
- Must be true: (b)
The common mistake
The mistake
If a statement could be true, choose it.
Instead
Only choose what must be true from the facts given.
Why: In logic questions, 'could be true' answers are traps: one missing fact makes them uncertain.
Where it comes up in the 11+
Letter sums and logic problems are GL verbal reasoning types. CEM-style tests use similar logic in maths and reasoning.
The video
Video coming soon
We're making a short video that explains letter sums and logic problems step by step. Until then, everything it covers is on this page.
Free printable
Letter sums and logic problems worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
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Quick quiz
Have a go first, then tap to see the answer.
1. A = 3, B = 5, C = 8, D = 15, E = 2. What is A × B, as a letter?
- D
- C
- B
- E
Show the answerHide the answer
D
3 × 5 = 15, which is D.
2. A = 6, B = 2, C = 3, D = 4, E = 12. What is A ÷ C + B, as a letter?
- D
- B
- C
- E
Show the answerHide the answer
D
6 ÷ 3 = 2, then 2 + 2 = 4, which is D.
3. Amy is taller than Ben. Ben is taller than Cal. Who is the shortest?
- Cal
- Ben
- Amy
- You can't tell
Show the answerHide the answer
Cal
Amy, then Ben, then Cal.