HSPT: Logic: what all, no and some guarantee
Decide which conclusion must follow from statements that use all, no or some, and avoid reversed and overreaching choices.
How do you tell which conclusion must follow from statements with all, no or some?
Short answer
Apply each statement exactly as written, in the direction it's written, and chain statements that share a group. A conclusion must follow only if the statements force it.
Know first: The difference between must and might, Reading each word of a statement carefully
Step 1 of 5
Each quantifier makes a precise promise
Some HSPT logical reasoning questions give two or three statements and ask which conclusion must follow. Treat the statements as true, even if they sound odd, and use nothing beyond them.
Most of these statements use all (or every), no, or some. Each one promises something exact, and each has a reversal that sounds right but isn't guaranteed.
| Statement | Guarantees | Does not guarantee |
|---|---|---|
| All owls are birds. | Any owl is a bird. | Any bird is an owl. |
| No fish are mammals. | No mammal is a fish. No works both ways. | Every animal that isn't a mammal is a fish. |
| Some students are left-handed. | At least one student is left-handed. | Every student is left-handed. It also doesn't prove that some students are not left-handed. |
All runs one way only. Reading it backward is the most common wrong answer.
Step 2 of 5
Chain two statements to a conclusion
Worked example: Hikers and water
Assume these statements are true. All of the hikers in the group carried water. No one who carried water felt faint. Which conclusion must follow?
- ASome hikers in the group felt faint.
- BAll the people who carried water were hikers in the group.
- CNo hiker in the group felt faint.
- DThe hikers walked a long way.
- 1
Write the chain
Hiker in the group → carried water. Carried water → did not feel faint.
- 2
Follow it
Every hiker carried water, and no one who carried water felt faint. So no hiker in the group felt faint.
- 3
Why the others are there
The first choice contradicts the chain. The second reverses the first statement: other people could have carried water too. The last adds a fact about distance that the statements never give.
Answer
No hiker in the group felt faint. The chain forces it.
Wrong: All violinists in the orchestra read music. Kai reads music. So Kai is a violinist in the orchestra.
Right: All violinists in the orchestra read music. Kai is a violinist in the orchestra. So Kai reads music.
The statement runs from violinist to music reader. Reading music doesn't put someone in the orchestra, since plenty of readers play other instruments or none.
Step 3 of 5
Find what must follow
Check yourself · Question 1
Assume these statements are true. No trains on the express line stop at Elm Street. The 7:15 train is on the express line. Which conclusion must follow?
Answer: A
The no statement covers every express train, and the 7:15 is one of them. So it does not stop at Elm Street.
Check yourself · Question 2
Assume these statements are true. Some of the club's paintings are watercolors. All watercolors in the club are framed in wood. Which conclusion must follow?
Answer: B
Some + all chains to some: the paintings that are watercolors are framed in wood, so at least some paintings are framed in wood.
Trap answer: All of the club's paintings are framed in wood.
Some turned into all
- Why it looks right
- The second statement says all, so the conclusion feels as if it should say all too.
- Why it's wrong
- That all covers watercolors only. Since only some paintings are watercolors, only some paintings are guaranteed wood frames.
- The right answer
- Some of the club's paintings are framed in wood, which is exactly as far as the chain reaches.
Check yourself · Question 3
Assume these statements are true. No sculptures in the hall are made of glass. Some objects in the hall are sculptures. Which conclusion must follow?
Answer: D
The sculptures in the hall aren't glass, and some objects in the hall are sculptures. So at least some objects in the hall aren't glass.
Common mistake
Reading all A are B as if it also meant all B are A.
- Why it's tempting
- Plenty of everyday facts happen to work both ways, so the reversal sounds natural.
- Do this instead
- Picture an arrow from A to B and travel only that way. Only no and some statements work in both directions.
Step 4 of 5
What to remember
Remember
- Use only the statements given, and apply each one exactly as written.
- All runs one way. No and some work both ways.
- Chain statements that share a group, and stop where the chain stops.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
Which statement in the practice question did you apply, and which wrong choice read a statement backward?