Problem Solving and Logic Set C
Problem Solving and Logic Set C is a practice set of logic-based word problems for the 11+ maths and numerical reasoning paper, covering deduction puzzles, elimination grids and multi-clue 'who is who' problems. These items test careful reading and systematic working rather than calculation, and they appear on GL Assessment and CEM style papers as short reasoning questions.
Method
- List every clue given in the problem as a short separate statement before trying to solve anything.
- Draw a simple grid or table when the problem compares multiple people, items or categories, ticking or crossing cells as clues rule things in or out.
- Start with the most restrictive clue, the one that rules out the most possibilities, rather than the first clue in the text.
- Work through the remaining clues one at a time, updating the grid, and re-check earlier deductions each time a new fact is added.
- When a clue gives a numerical relationship, such as 'older than' or 'twice as many as', turn it into a short equation or list of possible values before combining it with other clues.
- Once every cell in a grid has exactly one tick, state the answer in a full sentence and check it against every original clue.
Worked example
Three friends, Ali, Ben and Cara, each have a different pet: a cat, a dog or a rabbit. Ali does not have the dog. Ben does not have the rabbit. Cara does not have the rabbit or the cat. Work out which pet each friend has.
- List the clues: Ali is not the dog owner; Ben is not the rabbit owner; Cara is not the rabbit owner or the cat owner.
- Cara cannot have the rabbit or the cat, so by elimination Cara must have the dog.
- Since Cara has the dog, this is consistent with Ali not having the dog.
- The only pets left for Ali and Ben are cat and rabbit. Since Ben does not have the rabbit, Ben must have the cat, leaving Ali with the rabbit.
- Check every clue: Ali has the rabbit (not the dog, correct); Ben has the cat (not the rabbit, correct); Cara has the dog (not the rabbit or the cat, correct).
- Final answer: Ali has the rabbit, Ben has the cat, and Cara has the dog.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Four children are in a race: Amy finishes before Ben. Ben finishes before Cleo. Dan finishes after Cleo. List the finishing order.Show answer
Answer: Amy, Ben, Cleo, Dan
Q2A is older than B. B is older than C. Is A older or younger than C?Show answer
Answer: Older
Q3In a row of three houses, the red house is not at either end. The blue house is to the left of the red house. What colour is the middle house?Show answer
Answer: Red
Q4Three boxes are labelled Apples, Oranges and Mixed, but all the labels are wrong. If you can draw only one fruit from one box, from which box should you draw to work out the true contents of all three boxes, and why?Show answer
Answer: The box labelled Mixed, since every label is wrong, this box must contain only apples or only oranges, and knowing which one lets you deduce the true contents of the other two boxes
Q5In a class, everyone who plays chess also plays draughts. Maya plays chess. Does Maya play draughts?Show answer
Answer: Yes, since everyone who plays chess also plays draughts, and Maya plays chess
Q6In a group of three friends, X is taller than Y, and Z is shorter than Y. Who is the tallest?Show answer
Answer: X
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Four friends, Priya, Raj, Sam and Tia, each scored a different amount in a quiz: 10, 12, 14 and 16 points. Raj scored more than Priya. Sam scored the highest of the four. Tia scored 12 points. Work out each person's score, showing your reasoning.
Show mark scheme
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Nothing ticked yet - 4 available
In a row of four houses numbered 1 to 4, each is painted a different colour: red, blue, green or yellow. House 2 is green. The red house is immediately to the right of the blue house. The yellow house is at one end. House 4 is not yellow. Find the colour of each house, explaining your reasoning.
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the problem solving and logic set c worksheet pack - 10 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 6 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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