Verbal Reasoning: Logic Set 5
Verbal Reasoning: Logic Set 5 is the final and hardest practice round on deduction puzzles in this collection, combining longer chains of comparison statements with four-way grid puzzles matching several people to two separate categories at once, and 'all', 'some' and 'no' statements used together, so a pupil must hold several linked pieces of reasoning in mind rather than solving one simple step.
Method
- List every statement given as a short separate fact first, numbering them if it helps, before attempting to combine any two of them.
- For a grid puzzle with two categories, such as four people each having one sport and one favourite colour, draw a grid with a row for each person and a column for each possible value in both categories, then cross off every combination a statement rules out.
- Fill in any value that is stated directly first, then use each newly confirmed fact to cross that same value off every other row, since no two people share a value in these puzzles.
- For 'all', 'some' and 'no' statements used together, work out exactly what each one guarantees on its own before combining them; a statement that a group does something does not automatically mean everyone who does that thing belongs to the group.
- For a chain of comparisons involving more than four people, build the chain in stages, checking after each new statement whether it extends the existing chain, starts a separate chain, or fills a gap inside the chain you already have.
- Before giving your final answer, check it against every single statement given, not only the ones you used to build it, since a fully correct-looking chain or grid can still break one overlooked clue.
Worked example
All the pupils on the chess team practise on Tuesdays. Some pupils on the chess team also play in the school orchestra. Priya practises on Tuesdays. Can you conclude that Priya is on the chess team?
- Restate what the first statement guarantees: every pupil on the chess team practises on Tuesdays, which means practising on Tuesdays is a result of being on the chess team, not the other way round.
- Check whether the statement also guarantees the reverse, that everyone who practises on Tuesdays is on the chess team: it does not, since other pupils could also practise on Tuesdays for an unrelated reason.
- Apply this to Priya: knowing that Priya practises on Tuesdays does not prove she is on the chess team, because the first statement never claims that Tuesday practice is unique to the chess team.
- Note that the second statement about the orchestra does not help either, since it only tells us that some chess team members play in the orchestra, not who counts as being on the chess team in the first place. Final answer: Cannot tell - practising on Tuesdays does not prove Priya is on the chess team.
Practice questions
Try each question, then tap to reveal the answer.
Q1Aiden is older than Bea. Bea is older than Cade. Dara is older than Aiden. Cade is older than Emil. Is Dara older or younger than Emil, and how do you know?Show answer
Answer: Dara is older than Emil, since the full chain from oldest to youngest is Dara, Aiden, Bea, Cade, Emil.
Q2Four pupils, Amir, Bea, Cody and Dee, each have a different favourite subject: maths, art, science or music. Amir's favourite is not maths or science. Bea's favourite is not art or music. Cody's favourite is not music. Dee's favourite is science. What is Amir's favourite subject?Show answer
Answer: Music - Dee has science, Bea must have maths, Cody must have art (since music is ruled out and maths and science are taken), leaving music for Amir.
Q3No pupil in Year 5 has a packed lunch on Fridays. Which of these statements must be FALSE? A) Every Year 5 pupil has a school dinner on Fridays. B) Zara, who is in Year 5, has a packed lunch on Friday. C) Some Year 6 pupils have a packed lunch on Friday. D) No Year 5 pupil has a school dinner on Friday. E) Zara is not in Year 5.Show answer
Answer: B) Zara, who is in Year 5, has a packed lunch on Friday - this directly contradicts the given statement that no Year 5 pupil has a packed lunch on Fridays.
Q4Farah is taller than Grace. Hugo is taller than Ivy. Grace is taller than Jax. Is Hugo taller or shorter than Jax, or can this not be determined?Show answer
Answer: Cannot tell - the statements never compare Hugo's pair with Jax's group, so there is no link between the two chains.
Q5All members of the art club use the workshop on Mondays. Leo uses the workshop on Mondays. Priya is a member of the art club. What can you definitely conclude about Priya, and what can you NOT definitely conclude about Leo?Show answer
Answer: Priya definitely uses the workshop on Mondays, since all art club members do; Leo cannot definitely be concluded to be an art club member just from using the workshop on Mondays, since other pupils might use it too.
Q6Three pupils, Kofi, Lily and Marco, each play one sport (netball, tennis or hockey) and each was born in a different month (April, May or June). The hockey player was born in May. Kofi was born in April. Lily does not play hockey. Kofi does not play tennis. What sport does Kofi play, and what sport does Marco play?Show answer
Answer: Kofi plays netball and Marco plays hockey - Kofi cannot play hockey since the hockey player was born in May and Kofi was born in April, and Lily does not play hockey either, so Marco plays hockey; Kofi does not play tennis, so Kofi plays netball, leaving tennis for Lily.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Four pupils, Ana, Ben, Cara and Dev, each play exactly one sport (football, netball, tennis or hockey). The hockey player's favourite colour is green. Ana's favourite colour is red. Ben plays football. Cara's favourite colour is not blue or yellow. Dev plays tennis. Work out each pupil's sport, and state which colour Cara's favourite must be.
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Every member of the gardening club waters the plants on Saturdays. Some members of the gardening club also help at the school fair. Noah waters the plants on Saturdays. Can you conclude that Noah is a member of the gardening club? Explain your reasoning in full.
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Six athletes compare their race times. Farrah finished before Grant. Grant finished before Hana. Ibrahim finished before Farrah. Hana finished before Jade. Kian finished after Jade. Put all six athletes in order from first to last, and state who finished fourth.
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Free printable worksheet
Want more practice on paper? Download the verbal reasoning: logic set 5 worksheet pack - 15 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 29 of 11+ Verbal Reasoning Workbook 3, the whole course as one free printable PDF.
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