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?

• AThe chess club has exactly eleven members in total this year
• BAll members of the school play chess at some point in the school chess club
• CSome members of the chess club are under the age of eleven
• DNo member of the chess club is under the age of eleven✓

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
• BCustomers said they liked the new logo
• CA major competitor went out of business at the same time✓
• DThe company has changed its logo before

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 does not train enough to be picked for the team
• BOnly athletes who are on the team train every single day of the week
• CSam may or may not be an athlete on the team✓
• DSam must therefore be an athlete on the team as well

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 did not rain✓
• BThe match was a draw
• CThe match will be rescheduled
• DIt rained

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 toothpaste is sold in many different countries around the world today
• BThe dentists who were surveyed all use the toothpaste themselves at home
• CThe dentists were asked to compare it against all rival toothpastes✓
• DThe tenth dentist in the survey was not properly qualified to give any opinion

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?

• ASome books in the shop are discounted✓
• BAll discounted books in the shop are second-hand
• CAll of the books in the shop are discounted books
• DNo new books are discounted

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?

• AThe student should have revised for twenty hours rather than only ten
• BOne person's result does not prove revision is generally pointless✓
• CThe exam was unfair to every one of the students who sat it in that hall
• DTen hours is far too much revision for anyone to do before one written exam

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 a registered voter
• BMaria voted by post
• CMaria is not a registered voter✓
• DMaria must have lost her polling card in the 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 new speed cameras cost the council to buy and to install?
• BDo drivers like the cameras?
• CWere there other road changes, such as new signs, made at the same time?✓
• DWho manufactured the speed cameras that were installed on this stretch of road?

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?

• ARefunds might also be given for reasons other than complaints✓
• BThere is no flaw in the reasoning at all; the conclusion follows
• 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 divisible by 6
• B21 is an even number
• C21 is not divisible by 3
• DWe cannot conclude whether 21 is divisible by 3 from this statement alone✓

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.

Everyone who passed the exam celebrated. Tom celebrated. Which statement is logically supported?

• ANobody who failed the exam celebrated anything afterwards
• BTom passed the exam
• CIt is possible Tom passed, but it cannot be concluded✓
• DTom did not pass the exam

Answer: Passing leads to celebrating, but people may celebrate for other reasons, so Tom's passing cannot be concluded.

A health blog argues: 'People who drink green tea live longer, so drinking green tea makes you live longer.' Which possibility most weakens this argument?

• AGreen tea tastes pleasant
• BSome people prefer coffee
• CGreen-tea drinkers may also tend to have healthier lifestyles overall✓
• DGreen tea is widely available

Answer: If green-tea drinkers also live more healthily in other ways, those habits, not the tea, could explain the longer lives.

All the fruit in the basket is ripe. Some of the fruit in the basket is sweet. Which conclusion must be true?

• AAll ripe fruit is sweet
• BNo ripe fruit is sweet
• CSome ripe fruit in the basket is sweet✓
• DAll sweet fruit is in the basket

Answer: Since all basket fruit is ripe and some is sweet, that sweet fruit is both ripe and sweet.

A politician claims: 'Most people I spoke to at the rally support the new policy, so most voters support it.' Which is the main weakness of this argument?

• ARallies are held outdoors
• BThe new policy is too complicated for most ordinary voters to follow
• CThe politician spoke too quickly for the crowd at the rally to hear
• DThe rally attendees are likely not representative of all voters✓

Answer: People at a rally for a policy are a biased sample, so their views cannot be generalised to all voters.

If the alarm sounds, the doors lock automatically. The doors did not lock. Which conclusion is valid?

• ASomeone unlocked the doors
• BThe alarm did not sound✓
• CThe alarm sounded
• DThe doors are broken

Answer: The alarm sounding always locks the doors; since they did not lock, the alarm did not sound.

A manager reasons: 'Team A finished the project faster than Team B, and Team A used the new software. Therefore the new software makes teams faster.' Which fact would most weaken this conclusion?

• AThe project had a fixed deadline that was agreed in advance
• BTeam B also wanted to use the new software package
• CTeam A had twice as many members as Team B✓
• DThe new software is popular

Answer: A much larger team size offers an alternative explanation for Team A's speed, undermining the software claim.

No member of the orchestra plays the drums. Priya plays the drums. Which conclusion must be true?

• APriya must therefore be a member of the orchestra
• BPriya is not a member of the orchestra✓
• CThe orchestra has no percussion
• DPriya plays other instruments too

Answer: No orchestra member plays drums, and Priya does, so Priya cannot be an orchestra member.

A survey of website visitors found that 80% rated the site 'excellent'. The site owner concludes that 80% of all internet users would rate it excellent. What is the flaw?

• AThe survey should have used a five-point rating scale instead of words on their own
• BWebsites cannot really be rated by the people who visit them in any meaningful way at all
• CEighty percent is far too high a proportion for most people to find at all believable
• DThe survey only sampled people who already visit the site, not all internet users✓

Answer: Visitors are a self-selected, favourable sample and cannot represent all internet users.