Logic
A few short facts compare people, and you work out who is fastest, tallest or first, or what must be true. Here's how to get it right, and how to spot when it's Can't tell.
Chapter 1
What are logic questions?
You get two or three short facts that compare people: who is taller, older or faster, whose bag is heavier, who arrived first. Then a question asks about the order.
You work it out from the facts alone. Often one option is Can’t tell, and sometimes it’s right: when the facts don’t decide it.
The facts. Each one compares two people.
The question. Who is at the top of the order, the bottom, or in the middle?
The answers. Four in Rush, five in the exam. Can’t tell is often one of them.
Chapter 4 covers the longer puzzles some papers set, like which statement must be true.
Nia is slower than Bea. Isla is slower than Nia.
Who is the fastest?
- Option 1: Can’t tell
- Option 2: Isla
- Option 3: Bea
- Option 4: Nia
A Verbal question from Rush, level 1.
Every fact can be said two ways
The words come in pairs. Swap the names and swap the word, and the fact still means the same: Nia is slower than Bea is the same as Bea is faster than Nia.
- taller↔ and shorter
- older↔ and younger
- faster↔ and slower
- heavier↔ and lighter
- before↔ and after
- earlier↔ and later
Chapter 2
Solve it in 4 steps.
Here’s the question, one step at a time.
The question
Nia is slower than Bea. Isla is slower than Nia.
Who is the fastest?
- Option 1: Can’t tell
- Option 2: Isla
- Option 3: Bea
- Option 4: Nia
A Verbal question from Rush, level 1.
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Step 1
Find which end you need.
Read the question before the facts. Fastest is the top of the order. Slowest would be the bottom.
Who is the fastest?
You need the top.
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Step 2
Turn every fact the same way.
Both facts say slower, but you want fastest. Swap the names and swap the word, and both facts say faster.
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Step 3
Line them up, one fact at a time.
Fastest at the top. The first fact puts Bea above Nia. The second puts Isla under Nia. On paper, write the names in a column.
Fact 1 Fact 2 -
Step 4
Check nobody could swap.
Two people could swap places if no fact puts one above the other. Here one chain runs from top to bottom, so nobody can. Bea is the fastest for certain.
One chain: nobody can swap.
The three wrong answers
| The mistake | Do this instead |
|---|---|
| Answering the word in the facts. The facts keep saying slower, so Isla, the slowest, feels right. In about a third of Rush’s easier questions, the question uses the other word. | Find which end the question wants before you read the facts. |
| Reading a fact backwards. Read “Nia is slower than Bea” as if Nia wins, and Nia ends up on top. | Turn each fact round and say it: Bea is faster than Nia. |
| Picking Can’t tell to be safe. All three are in one chain, so the order is fixed. | Pick Can’t tell only when you can name two people who could swap. |
So it’s Bea. Bea is faster than Nia, and Nia is faster than Isla, so nobody beats Bea.
Remember: Which end? Turn, line up, check.
Chapter 3
When it gets harder.
Rush’s harder level gives three facts about four people and mixes the words up. Turn them all the same way first, then use these.
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Two could swap? Can’t tell
If two people could swap at the spot you need, it’s Can’t tell.
Uma is shorter than Wes. Uma is taller than Musa. Ben is taller than Uma. Who is tallest? Wes and Ben are both above Uma, but no fact compares them. Trap: picking Wes because he comes first. He might be tallest, and might isn’t enough.
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Someone left loose? Answer the spot asked
A person you can’t place only matters if they could take your spot.
Zak is faster than Ada. Lola is slower than Eli. Ada is faster than Lola. Who is slowest? Eli could be anywhere above Lola, but nobody is below her: it’s Lola. Trap: Can’t tell, because Eli’s place is unclear.
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Middle or second: you need the whole line
With three people, the middle one is above one and below the other.
Uma is shorter than Kai. Kai is shorter than Ian. Kai is in the middle. Trap: Nia and Lily are both faster than Omar. Who is in the middle? Nia or Lily, so it’s Can’t tell. Who arrived second works the same way.
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In your head: who never loses?
Once every fact says taller, the tallest is the only name that never comes after than.
Isla is shorter than Rosa. Wei is shorter than Isla. Isla is taller than Leo. Turned round, only Rosa never loses, so she’s the tallest. Trap: for the shortest, find who never wins. That’s Wei and Leo, two names, so it’s Can’t tell.
Chapter 4: In the exam
Longer puzzles: what must be true?
Many papers set one or two logic questions longer than Rush’s, with five statements to choose from. Rush doesn’t ask these, but drawing the facts still cracks them.
The questionFive friends ran a race. Dev finished before Asha. Asha finished before Ben. Cara finished after Ben. Eli finished after Asha. Which one of these must be true?
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Step 1
Draw it, one fact at a time.
First at the top. Dev goes above Asha, Ben under Asha, Cara under Ben. Eli is under Asha, but no fact compares him with Ben or Cara, so he goes to one side.
Eli could be 3rd, 4th or 5th.
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Step 2
Mark each option: certain or only possible?
Must be true means true in every order the facts allow. Only C is: everyone but Dev comes after Asha. A and B could happen, but Eli could just as well be third.
Three traps in the options
| The mistake | Do this instead |
|---|---|
| Picking what could be true. Eli might finish last, and Ben might be third. Might isn’t must. | Find another order that fits the facts. If the option fails in it, it’s out. |
| Reading a fact backwards. Cara finished after Ben means Ben beat Cara, so D has it the wrong way round. | Turn each fact into your line’s word: Ben finished before Cara. |
| Using a fact that isn’t given. Dev won this race, but nothing says he’s the fastest in the school. | Use only the facts, never what you know or guess. Something new in an option is a warning sign. |
So it’s C. Dev is the only one before Asha, so she’s second in every order the facts allow.
Remember: Must means no other way.
Other ways the exam asks it
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dog cat fish Amy ✗no ✓yes ✗no Ben ✗no ✗no ✓yes Cal ✓yes ✗no ✗no Who has what? Draw a grid
Names down the side, things across the top. One tick in each row and column.
Amy, Ben and Cal have a dog, a cat and a fish. Ben has the fish. Amy doesn’t have the dog. Who has the cat? Amy can’t have the fish, which is Ben’s, or the dog, so she has the cat. Trap: stopping too soon. The last answers come from the crosses.
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Days and times: write them in order
Write the days down, and label each one as you read.
The day before yesterday was Thursday. What day is it tomorrow? Count on: Friday is yesterday, Saturday is today, so tomorrow is Sunday. Trap: counting from Thursday as if it were today. Clocks that run fast or slow work the same way: put the times on a line.
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Which cannot be true?
Now hunt for the one that breaks a fact. Ones that could be true are wrong this time.
Ali is older than Bo. Bo is older than Cy. Which cannot be true? Cy is older than Ali: the line puts Ali above Cy. Trap: missing the not. Underline cannot, not or false before you start.
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All, some and none
All means every one. Some means at least one, maybe not all.
Everyone in Class 6 walks to school. Some of them have a dog. Sam is in Class 6. Certain: Sam walks to school. Only possible: Sam has a dog. None works like all: if no one in Class 6 has a cat, Sam hasn’t. Trap: reading some as if it said all.
Chapter 5
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Find which end you need.
- Turn every fact the same way.
- Line them up, one fact at a time.
- Check nobody could swap.
Remember: Which end? Turn, line up, check.
For parents.
What parents ask us about logic.
Questions parents ask
What are logic questions in 11+ verbal reasoning?
Short puzzles where your child reads a few facts and works out what follows: who is oldest, who arrived first, or which statement must be true. They test careful reading more than knowledge.
When is Can't tell the right answer?
When two people could sit in the answer's spot without breaking any fact. Choose it once you can name those two people, never as a fallback when a question feels hard.
Should my child draw a diagram?
On paper, yes. A column of names, filled in as each fact is read, is quick to jot down and stops slips. Rush's questions are short enough to picture in your head, which builds the same line-up habit.
How can we practise logic at home?
Make up line-ups from your own family: Mum is older than Sam, and Sam is older than Ella, so who is youngest? Take turns setting them. Now and then leave out a fact, so the right answer is Can't tell. Saying each fact the other way round (Ella is younger than Sam) builds the habit these questions need.
Rush: 11+ Practice & KS2 SATsPractise logic in Rush.
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