What the question looks like
You are given two to four statements, then five conclusions. For each one you drag Yes if it follows and No if it does not. All five right earns two marks; four right earns one.
The one test that settles every conclusion
A conclusion follows only if it must be true in every situation the statements allow. If you can imagine one situation where the statements are true and the conclusion is false, the answer is No, however likely the conclusion sounds.
What each word means
| Statement | What it tells you | What it does not tell you |
|---|---|---|
| All A are B | Every A is a B. | That every B is an A. There may be B that are not A. |
| No A are B | No A is a B, and no B is an A. | Anything about things that are neither. |
| Some A are B | At least one A is a B, so at least one B is an A. | That some A are not B. "Some" can mean all. |
| Some A are not B | At least one A is outside B. | That some B are not A, or that some A are B. |
| Most A are B | More than half of A are B, so some A are B. | That most B are A. |
| Only A are B | Every B is an A. | That every A is a B. |
| If A, then B | Whenever A holds, B holds. If B does not hold, A does not. | That B means A. B can happen without A. |
Chains that work, and chains that do not
Most conclusions join two statements through a middle group. Four patterns cover nearly all of them.
| Given | You can conclude | Follows? |
|---|---|---|
| All A are B. All B are C. | All A are C. | Yes |
| All A are B. No B are C. | No A are C. | Yes |
| Some A are B. All B are C. | Some A are C. | Yes |
| Some A are B. No B are C. | Some A are not C. | Yes |
| Some A are B. Some B are C. | Some A are C. | No: the two "some" may be different members of B. |
| All A are B. Some B are C. | Some A are C. | No: the B that are C may all lie outside A. |
| All A are B. All C are B. | Some A are C. | No: two groups inside B need not overlap. |
| Most A are B. Most B are C. | Some A are C. | No: B may be far larger than A. |
One pattern with most does work: if most A are B and most A are C, then some A are both B and C, because two majorities of the same group must overlap.
A worked example
Original example: five conclusions
All the tutors at Marlow College hold a teaching certificate. Some of the tutors also coach sport. No one who coaches sport at the college works on Sundays. Most people at the college who hold a teaching certificate have worked there for over five years.
Place Yes if the conclusion follows. Place No if it does not.
- Some people who hold a teaching certificate coach sport.
- Everyone at the college who holds a teaching certificate is a tutor.
- Some tutors do not work on Sundays.
- Most tutors have worked at the college for over five years.
- No tutor works on Sundays.
Answer: Yes, No, Yes, No, No
1. Yes. Some tutors coach sport, and every tutor holds a certificate, so those tutors are certificate holders who coach.
2. No. "All tutors hold a certificate" does not run backwards. Other staff may hold one too.
3. Yes. The tutors who coach sport cannot work on Sundays, and there is at least one of them.
4. No. "Most" is said of certificate holders, not of tutors. Tutors might be a small part of that group, and all of them new.
5. No. Only the tutors who coach are ruled out of Sundays. Nothing is said about the others.
A method that takes under a minute
- Sketch the groups. A circle inside a circle for "all", two separate circles for "no", an overlap for "some". Ten seconds on the notebook saves holding it in your head.
- Take each conclusion alone. Ask whether it must be true, and look for one case where it is false.
- Watch for a statement turned around. The commonest wrong conclusion is "all A are B" restated as "all B are A".
- Use nothing from outside. If the statements say all birds in the question can swim, they can. What you know about real birds does not count.
- Answer all five. Four right still earns a mark, so never leave one blank.
Where marks are lost
- Reading "some" as "some but not all". In logic, some means at least one.
- Accepting a conclusion because it is probably true. Likely is not the same as certain.
- Carrying "most" across two statements.
- Missing a "not" or an "only" when reading quickly.
Practise them
Syllogisms reward repetition more than any other kind of Decision Making question, because the same few patterns come back. Do twenty untimed, checking each conclusion against the tables above, then start timing yourself at about a minute a question. Try free Decision Making questions, or read the full Decision Making guide for the other five kinds.
Official sources
Dates, fees and entry rules change every year. Always confirm them on the official page before you act on them.