Critical reasoning

All members of the chess club are also members of the school. No member of the school is under the age of eleven. Which conclusion must be true?

• ANo member of the chess club is under the age of eleven✓
• BSome chess club members are under eleven
• CAll school members play chess
• DThe chess club has exactly eleven members

Answer: Chess club members are school members, and no school member is under eleven, so no chess club member is under eleven.

A manager argues: 'Our sales rose after we changed the logo, so the new logo caused the increase.' Which of the following, if true, most weakens this argument?

• AThe new logo was designed by a famous studio
• BA major competitor went out of business at the same time✓
• CThe company has changed its logo before
• DCustomers said they liked the new logo

Answer: A competitor closing offers an alternative cause for the sales rise, undermining the claim that the logo caused it.

Every athlete on the team trains daily. Sam trains daily. Which conclusion is logically valid?

• ASam is an athlete on the team
• BSam may or may not be an athlete on the team✓
• CSam does not train enough
• DOnly athletes train daily

Answer: Training daily is true of all team athletes, but others may also train daily, so Sam's membership cannot be concluded.

If it rains, the match is cancelled. The match was not cancelled. Which conclusion must be true?

• AIt rained
• BIt did not rain✓
• CThe match was a draw
• DThe match will be rescheduled

Answer: Rain guarantees cancellation; since the match was not cancelled, it cannot have rained.

An advertisement states: 'Nine out of ten dentists recommend our toothpaste.' Which assumption is necessary for this to support the claim that the toothpaste is the best on the market?

• AThe dentists were asked to compare it against all rival toothpastes✓
• BThe toothpaste is sold in many countries
• CDentists use the toothpaste themselves
• DThe tenth dentist is unqualified

Answer: Being recommended says nothing about being best unless dentists actually compared it against all rivals.

Some books in the shop are second-hand. All second-hand books are discounted. Which conclusion must be true?

• AAll books in the shop are discounted
• BSome books in the shop are discounted✓
• CNo new books are discounted
• DDiscounted books are all second-hand

Answer: Some books are second-hand and all such books are discounted, so at least some books in the shop are discounted.

A student argues: 'I revised for ten hours and still failed, so revision is pointless.' Which is the strongest objection to this reasoning?

• ATen hours is too much revision for anyone
• BOne person's result does not prove revision is generally pointless✓
• CThe exam was unfair
• DThe student should have revised for twenty hours

Answer: Drawing a general conclusion from a single case is a flawed generalisation; one failure does not establish that revision is pointless.

All registered voters received a polling card. Maria did not receive a polling card. Which conclusion is valid?

• AMaria is not a registered voter✓
• BMaria is a registered voter
• CMaria lost her polling card
• DMaria voted by post

Answer: All registered voters received cards; Maria received none, so she cannot be a registered voter.

A columnist writes: 'Since the new speed cameras were installed, accidents on this road have fallen, so the cameras work.' Which question most challenges the argument?

• AHow much did the cameras cost to install?
• BWere there other road changes, such as new signs, made at the same time?✓
• CWho manufactured the cameras?
• DDo drivers like the cameras?

Answer: If other changes happened simultaneously, they could explain the fall in accidents, weakening the claim that cameras alone caused it.

No reptiles are warm-blooded. All snakes are reptiles. Which conclusion must be true?

• ASome snakes are warm-blooded
• BNo snakes are warm-blooded✓
• CAll warm-blooded animals are snakes
• DSome reptiles are snakes only

Answer: Snakes are reptiles and no reptile is warm-blooded, so no snake is warm-blooded.

A shop owner says: 'Every customer who complained received a refund. Therefore, anyone who received a refund had complained.' What is the flaw in this reasoning?

• AThere is no flaw; the conclusion follows
• BRefunds might also be given for reasons other than complaints✓
• CComplaints are never genuine
• DCustomers never receive refunds

Answer: The first statement does not say complaints are the only route to a refund, so a refund does not prove a complaint was made.

If a number is divisible by 6, it is divisible by 3. The number 21 is not divisible by 6. Which conclusion is valid?

• A21 is not divisible by 3
• B21 is divisible by 6
• CWe cannot conclude whether 21 is divisible by 3 from this statement alone✓
• D21 is an even number

Answer: The rule only tells us what follows from being divisible by 6; not being divisible by 6 tells us nothing certain about divisibility by 3.