How to Answer 11+ Deduction Questions
A deduction question gives you a block of facts — a timetable, some club rules, a bag of marbles — and five sentences. Find the one that must be true. They are the longest questions on the paper, but the wall of text is a toolkit: every line is a fact you will use to knock wrong sentences down.
Everything turns on one idea: could be true is not enough. If the facts say Sam has a dog, "Sam's dog is brown" could easily be true — but nothing forces it. A sentence must be true only if there is no way for it to be false while every fact holds. The test is never "does this sound right?" but "could I make this false without breaking a fact?"
The method
- Read the facts one at a time. A quiet rule at the end ("on Saturdays…", "at most…") often decides the answer.
- Start with the strongest clue. Exact numbers and times pin down the most; save vague words like "some" for last.
- Draw what you can. Line people up, sketch the timetable, count the marbles — paper beats memory.
- Try to break each sentence. Could it be false while the facts stay true? Then rule it out. The answer is the sentence left standing — and do the small sums twice on the way.
Worked examples
Example 1: could vs must
Read the following information carefully.
There are five pencils in Tilly's pencil case. Four of the pencils are sharpened.
If these statements are true, only one of the sentences below must be true. Which one?
A. All the pencils are sharpened. B. Exactly four of the pencils are sharpened. C. At least four of the pencils are sharpened. D. Only one of the pencils is sharpened.
The facts say nothing about the fifth pencil. Picture two worlds — fifth sharpened, fifth blunt — and test each sentence in both:
- A: true in one world, false in the other. Could be true; doesn't have to be. ✗
- B: false if the fifth pencil is sharpened too — that makes five. ✗
- C: four are definitely sharpened, so "at least four" holds in both worlds. ✓
- D: false everywhere: four are sharpened. ✗
The answer is C. At least four of the pencils are sharpened.
Example 2: timetables
Read this information carefully.
Trains run from Northgate to Southport, stopping at Westfield on every journey. Trains leave Northgate at 6.30 am, 8.30 am, 10.30 am, 12.30 pm, 2.30 pm and 4.30 pm. The journey from Northgate to Westfield takes 40 minutes. Westfield to Southport takes a further 25 minutes. On Saturdays, the 6.30 am and 8.30 am trains do not run.
All of the information above is true. Exactly one sentence below must be true as well — which one?
A. There are six trains from Northgate every day. B. The last train of the day leaves Northgate at 5.30 pm. C. The 10.30 am train arrives at Southport at 11.35 am. D. The train stops at two stations between Northgate and Southport. E. On Saturdays, the first train arrives at Westfield at 10.10 am.
Strongest clues first: the departure list and journey legs are exact.
- A: true Monday to Friday, but on Saturdays two trains are cut, leaving four. ✗
- B: the last departure in the list is 4.30 pm. ✗
- C: 10.30 am + 40 minutes = 11.10 am at Westfield, then + 25 minutes = 11.35 am at Southport. ✓
- D: only one stop, Westfield, sits between the two ends. ✗
- E: Saturday's first train is the 10.30 am, and it reaches Westfield at 11.10 am, not 10.10. ✗
The answer is C. The 10.30 am train arrives at Southport at 11.35 am.
Example 3: squeezing the numbers
Read this information carefully.
Twenty children go on a camping trip. The children take six tents. Each tent can sleep at most four children, and every child sleeps in a tent.
All of the information above is true. Exactly one sentence below must be true as well — which one?
A. Every tent is slept in. B. At least five of the tents are slept in. C. Exactly five of the tents are slept in. D. Two of the tents are empty. E. Every tent has at least three children in it.
Squeeze the numbers: four tents hold at most 4 × 4 = 16 children — not enough for 20.
- A: could be false: five full tents sleep all 20, leaving one empty. ✗
- B: forced: four tents can never hold 20. ✓
- C: could be false: the children could spread across all six. ✗
- D: false: at most one tent can ever be empty. ✗
- E: could be false: one tent might hold just two children. ✗
The answer is B. At least five of the tents are slept in.
The traps
- Could-be-true sentences. Four of the five usually sound sensible; some are even likely. Likely is still wrong. "Well, probably…" means cross it out.
- True on weekdays, wrecked at the weekend. One quiet line about Sundays can kill a sentence that holds all week — re-read the last fact before you commit.
- Arithmetic slips on times. 10.50 pm plus 15 minutes is 11.05 pm, not 11.10 pm. Crossing the hour is where the wrong options live — check those sums twice.
Try these yourself
1.
Read the following information carefully.
A tin holds twelve buttons. Five of the buttons are wooden and the rest are plastic.
If these statements are true, only one of the sentences below must be true. Which one?
A. There are more wooden buttons than plastic buttons. B. There are seven plastic buttons. C. There are six plastic buttons. D. Half of the buttons are wooden.
2.
Read the following information carefully.
Three tortoises crossed the lawn, finishing at different times. Sheldon finished before Truffle and before Pebble.
If these statements are true, only one of the sentences below must be true. Which one?
A. Truffle finished second. B. Pebble finished before Sheldon. C. Sheldon finished last. D. Truffle did not finish first.
3.
Read the following information carefully.
Ten beads are threaded on a string: seven are round and three are square. Four of the beads are red.
If these statements are true, only one of the sentences below must be true. Which one?
A. All the red beads are round. B. Exactly one of the round beads is red. C. At least one of the round beads is red. D. There are more square beads than round beads.
Answers
1. B: twelve buttons minus five wooden leaves exactly seven plastic.
2. D: Sheldon beat both of the others, so Sheldon was first and Truffle cannot have been.
3. C: only three beads are square, so the four red beads cannot all be square — one must be round.
Related
- The complete 11+ question-type guide
- How to answer 11+ logic problems — the other long question type.
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