Question 1 Syllogisms Every member of the chess club also belongs to the debating society. Some members of the debating society play in the school orchestra. Nobody who plays in the orchestra is in the drama group.
Which of the following conclusions follows from these statements?
Answer options for question 1 A Some members of the chess club play in the orchestra. B No member of the chess club is in the drama group. C Some members of the debating society are not in the drama group. D No member of the debating society is in the drama group.
Question 2 Logical puzzles Five runners – Amira, Ben, Chloe, Dev and Ellie – finished a race. There were no ties.
Dev finished ahead of Chloe, and Chloe finished ahead of Ben.
Amira finished immediately after Ben.
Ellie did not finish last.
Dev did not win.
Who finished second?
Answer options for question 2 A Amira B Ben C Chloe D Dev
Question 3 Strongest argument Should hospitals in the UK provide free car parking for patients attending outpatient appointments?
Select the strongest argument from the statements below.
Answer options for question 3 A Yes, because hospital car parks are often full at busy times of day. B Yes, because parking charges can add up to a large cost for patients who need frequent appointments, such as those having regular dialysis or cancer treatment. C No, because many patients travel to hospital by bus or train. D No, because people should always pay for everything they use.
Question 4 Venn diagrams A sixth-form college runs a science club and a coding club. Of its 80 students, 45 attend the science club, 30 attend the coding club and 12 attend both clubs.
How many of the 80 students attend neither club?
Answer options for question 4 A 5 B 12 C 17 D 29
Question 5 Probabilistic reasoning A bag contains 4 red, 5 blue and 3 green counters. Two counters are taken out at random, one after the other, without being put back.
What is the probability that both counters are blue?
Answer options for question 5 A 5 33 B 25 144 C 5 36 D 10 33
Question 6 Interpreting information Riverside Surgery publishes these rules for repeat prescriptions.
Requests can be made online or in writing. Telephone requests are accepted only from patients aged 75 or over, or from patients registered as housebound.
A prescription is ready to collect once two full working days have passed after the request is received. Working days are Monday to Friday.
Each medication review with a GP covers a patient's repeat prescriptions for 12 months. Once a review is overdue, one further repeat prescription can be issued; after that, no more can be issued until the review has taken place.
Which of the following conclusions can be drawn from the rules?
Answer options for question 6 A A patient aged 78 must make repeat prescription requests by telephone. B A request received on a Friday will be ready to collect on the following Monday. C A patient whose medication review became overdue last month cannot be issued any more repeat prescriptions until the review takes place. D A patient aged 52 who is registered as housebound may request a repeat prescription by telephone.
Question 7 Logical puzzles Four junior doctors – Fenna, Gita, Hugo and Ivan – each run one clinic, on different days from Monday to Thursday. The four clinics are asthma, diabetes, eczema and heart failure, one per doctor.
Hugo's clinic is on Thursday.
Fenna runs the eczema clinic, which is not on Monday.
The diabetes clinic is on the day immediately after Gita's clinic.
Ivan does not run the diabetes clinic.
The asthma clinic is earlier in the week than the heart failure clinic.
Who runs the heart failure clinic, and on which day?
Answer options for question 7 A Ivan, on Monday B Gita, on Tuesday C Hugo, on Thursday D Gita, on Wednesday
Question 8 Syllogisms Most of the paramedics at Northgate ambulance station have completed the advanced trauma course. Everyone who has completed the advanced trauma course has passed a driving assessment. Nobody who has passed a driving assessment is under 21.
Which of the following conclusions follows?
Answer options for question 8 A Most of the paramedics at Northgate are 21 or over. B All of the paramedics at Northgate have passed a driving assessment. C Some people who have passed a driving assessment are not paramedics at Northgate. D No paramedic at Northgate is under 21.
Question 9 Interpreting information The table shows the number of patients seen in a hospital's emergency department in each quarter of one year, by age group.
Which of the following statements is supported by the table?
Patients seen, by age group and quarter Quarter Under 18 18–64 65 and over Total Q1 2,400 6,100 3,500 12,000 Q2 2,100 6,400 3,000 11,500 Q3 1,800 6,900 2,800 11,500 Q4 2,700 6,000 3,900 12,600
Answer options for question 9 A The number of patients aged 18–64 rose in every quarter. B Under-18s made up more than a quarter of all patients seen during the year. C Patients aged 65 and over made up a larger share of the total in Q4 than in any other quarter. D The number of patients aged 65 and over rose by more than 40% from Q3 to Q4.
Question 10 Probabilistic reasoning Two fair six-sided dice are rolled and the two scores are multiplied together.
What is the probability that the product is an even number greater than 10?
Answer options for question 10 A 1 3 B 7 18 C 17 36 D 3 4
Question 11 Venn diagrams All of the surgeons at a hospital are doctors. Some of the doctors at the hospital are researchers. None of the surgeons is a researcher.
Each option describes a Venn diagram with three circles labelled Surgeons, Doctors and Researchers. Which diagram best represents the statements?
Answer options for question 11 A The Surgeons circle sits entirely inside the Doctors circle. The Researchers circle overlaps the Doctors circle but does not touch the Surgeons circle. B The Surgeons circle sits entirely inside the Doctors circle. The Researchers circle overlaps both the Doctors circle and the Surgeons circle. C The Surgeons circle and the Doctors circle partly overlap. The Researchers circle overlaps the Doctors circle but does not touch the Surgeons circle. D The Surgeons circle sits entirely inside the Doctors circle. The Researchers circle is completely separate from the Doctors circle.
Question 12 Recognising assumptions Since Westbridge introduced a 20 mph speed limit on its residential streets, the number of pedestrians injured on those streets has fallen by a third. Every town in the county should therefore introduce the same limit, and pedestrian injuries on residential streets across the county will fall by a third.
Which of the following is an assumption the argument relies on?
Answer options for question 12 A Every driver in Westbridge has kept to the new 20 mph limit. B Pedestrian injuries are the most serious road-safety problem in the county. C The new limit, rather than something else, caused the fall in Westbridge, and it would have a similar effect in other towns. D Westbridge had more pedestrian injuries than any other town in the county before the limit was introduced.
Question 13 Logical puzzles In a 20-question quiz, each correct answer scores 4 points, each wrong answer loses 1 point, and a question left unanswered scores 0.
Sana scored 51 points and left at least two questions unanswered.
How many questions did Sana answer wrongly?
Answer options for question 13 A 1 B 3 C 5 D 6
Question 14 Syllogisms No antibiotic in a pharmacy's stock is effective against viruses. Some of the medicines in stock that are effective against viruses are tablets. All tablets in stock are kept in the locked cabinet.
Which of the following conclusions follows?
Answer options for question 14 A No antibiotics are kept in the locked cabinet. B All tablets in stock are effective against viruses. C Some antibiotics in stock are tablets. D Some medicines in the locked cabinet are not antibiotics.
Question 15 Strongest argument Should large supermarkets be required by law to donate unsold edible food to charities instead of throwing it away?
Select the strongest argument from the statements below.
Answer options for question 15 A Yes, because charities that receive donated food are often run by volunteers who give up their own time. B Yes, because large amounts of edible food are thrown away while many households struggle to afford food, so donating it would cut waste and help people in need. C No, because some of the food supermarkets throw away has passed its use-by date and would not be safe to eat. D No, because supermarkets have always decided for themselves what to do with their unsold stock.
Question 16 Interpreting information These are the visiting rules on Maple Ward.
Visiting hours are 2 pm to 8 pm every day.
No patient may have more than two visitors at the bedside at any one time.
Children under 12 may visit only if they are with an adult, and only between 2 pm and 5 pm.
The nurse in charge may allow visits outside visiting hours for patients receiving end-of-life care.
Anyone with a cough or a high temperature must not visit.
Which of the following conclusions can be drawn from the rules?
Answer options for question 16 A A 10-year-old may visit at 6 pm as long as an adult comes too. B A patient may have three visitors at the bedside at once if one of them is a child. C A 14-year-old visiting alone at 7 pm, with no cough or temperature and nobody else at the bedside, would not break any of these rules. D No visits are ever allowed outside 2 pm to 8 pm.
Question 17 Venn diagrams A Venn diagram shows which of three subjects – biology, chemistry and maths – are studied by the 80 students in a year group. The table gives the number of students in each region of the diagram.
Which of the following statements is true?
Region of the diagram Students Biology only 14 Chemistry only 9 Maths only 21 Biology and chemistry only 11 Biology and maths only 6 Chemistry and maths only 8 All three subjects 5 None of the three 6
Answer options for question 17 A More students study chemistry than study biology. B More than half of the 80 students study exactly one of the three subjects. C More than half of the students who study maths also study at least one of the other two subjects. D Fewer than a third of the students who study biology also study chemistry.
Question 18 Probabilistic reasoning A clinic has 10 patients booked for one morning: 6 are new patients and 4 are returning patients. The receptionist chooses 3 of the 10 at random to fill in a feedback form.
What is the probability that exactly two of the three chosen are new patients?
Answer options for question 18 A 1 6 B 54 125 C 1 2 D 2 3
Question 19 Logical puzzles Six colleagues – Ava, Bilal, Cora, Dan, Esme and Femi – sit equally spaced around a circular table.
Ava sits directly opposite Dan.
Bilal sits next to both Ava and Esme.
Cora does not sit next to Dan.
Who sits directly opposite Femi?
Answer options for question 19 A Bilal B Cora C Esme D Dan
Question 20 Syllogisms Every member of the cycling club owns a helmet. Some people who own a helmet also own a skateboard. Nobody who owns a skateboard is under 10. Some members of the cycling club are under 10.
Which of the following conclusions follows?
Answer options for question 20 A Some members of the cycling club own a skateboard. B No member of the cycling club owns a skateboard. C Some people who own a helmet do not own a skateboard. D Everyone who owns a skateboard is a member of the cycling club.
Question 21 Interpreting information A hospital audits hand hygiene on three wards. Each observation is recorded as compliant or not compliant. The table shows the results for January and February.
Which of the following statements is supported by the data?
Ward January observations January compliant February observations February compliant A 80 68 120 96 B 50 45 40 34 C 100 70 90 72
Answer options for question 21 A The compliance rate fell on every ward from January to February. B Ward B had the lowest compliance rate in February. C Ward A recorded more compliant observations in February than Wards B and C put together. D Across the three wards combined, the compliance rate was higher in February than in January.
Question 22 Strongest argument Should GP surgeries in England charge patients a small fee for missing an appointment without cancelling it?
Select the strongest argument from the statements below.
Answer options for question 22 A Yes, because missed appointments waste clinical time that could have been given to other patients, and a fee would give people a reason to cancel in advance. B Yes, because some patients miss more than one appointment. C No, because patients sometimes simply forget their appointments. D No, because many surgeries already send text reminders before appointments.
Question 23 Venn diagrams In a group of 50 medical school applicants, 42 have done hospital work experience, 39 have volunteered in a care home and 36 have shadowed a GP.
What is the smallest possible number of applicants who have done all three?
Answer options for question 23 A 0 B 17 C 31 D 36
Question 24 Probabilistic reasoning A fundraising game costs £2 to play. A fair six-sided die is rolled once. A 6 wins £8, a 5 wins £3, and any other score wins nothing. The £2 is never returned.
Over a large number of games, what is a player's average result per game?
Answer options for question 24 A A profit of about 17p B No profit or loss C A loss of about 67p D A loss of about 17p
Question 25 Logical puzzles A four-digit door code uses four different digits, each from 1 to 9.
The first digit is twice the fourth digit.
The second digit is larger than each of the other three digits.
The third digit is a square number.
The four digits add up to 20.
What is the code?
Answer options for question 25 A 4862 B 6743 C 4952 D 6923
Question 26 Recognising assumptions About 40% of students at Hillside School use a new revision app. In their mock exams, students who used the app scored on average 12 marks more than students who did not. So the app improves exam results, and the school should pay for every student to have it.
Which of the following is an assumption the argument relies on?
Answer options for question 26 A The students who chose to use the app were not already likely to score higher than those who did not. B Using the app is the only way students can improve their mock exam marks. C The mock exams were harder this year than last year. D The app was designed by qualified teachers.
Question 27 Interpreting information Priya arrives at the bus station at 07:42 and needs to get to the hospital. Three bus routes run from the station to the hospital, as shown in the table. Buses leave exactly on time and take exactly the journey time shown.
What is the earliest time Priya can arrive at the hospital?
Route First bus leaves the station Then every Journey time to the hospital 7 07:10 20 minutes 25 minutes 12 07:05 35 minutes 15 minutes 21 07:20 30 minutes 20 minutes
Answer options for question 27 A 07:55 B 08:10 C 08:15 D 08:30
Question 28 Syllogisms In a hospital trust:
Every consultant supervises at least one trainee.
Nobody who supervises a trainee works part-time.
Some of the trust's surgeons work part-time.
Every surgeon in the trust is either a consultant or a registrar.
Which of the following conclusions follows?
Answer options for question 28 A Some consultants in the trust work part-time. B No registrar in the trust supervises a trainee. C All part-time staff in the trust are surgeons. D Some registrars in the trust work part-time.
Question 29 Probabilistic reasoning On any weekday, the probability that Tom's train to work is late is 0.2, independently of other days.
What is the probability, to two decimal places, that his train is late on at most one day in a five-day working week?
Answer options for question 29 A 0.26 B 0.33 C 0.41 D 0.74
Question 30 Strongest argument Should all new homes built in the UK be required to have solar panels?
Select the strongest argument from the statements below.
Answer options for question 30 A Yes, because solar panels show that a household cares about the environment. B No, because it is sometimes cloudy in the UK. C Yes, because fitting panels while a home is being built costs less than adding them later, and they would lower energy bills and carbon emissions for the life of the home. D No, because some people do not like the way solar panels look.
Question 31 Logical puzzles Five parcels, V, W, X, Y and Z, all have different weights.
V is heavier than W.
X is heavier than V but lighter than Y.
Z is heavier than W but lighter than X.
Which of the following must be true?
Answer options for question 31 A X is the second heaviest parcel. B Z is heavier than V. C V is the second lightest parcel. D W is heavier than Z.
Question 32 Venn diagrams A running club surveyed its 100 members about when they run.
48 run on Saturdays, 52 run on Sundays and 30 run on weekdays.
20 run on both Saturdays and Sundays, 12 run on both Saturdays and weekdays, and 10 run on both Sundays and weekdays. These figures include the 5 members who run on all three.
How many members run at none of these times?
Answer options for question 32 A 5 B 7 C 12 D 17
Question 33 Interpreting information A hospital trialled a new falls-prevention programme on two of its four elderly-care wards for six months. The two trial wards were chosen because they had recorded the most falls in the previous year.
On the two trial wards, the number of falls dropped from 48 in the six months before the trial to 30 during it. On the other two wards, which carried on as before, falls dropped from 40 to 34 over the same periods. Staffing levels were the same on all four wards throughout.
Which of the following conclusions is best supported by this information?
Answer options for question 33 A The programme reduced falls on the trial wards by 18. B The programme would reduce falls by the same proportion if it were introduced on the other two wards. C Part of the drop in falls on the trial wards might have happened even without the programme. D The programme had no effect on the number of falls.
Question 34 Logical puzzles Six candidates – K, L, M, N, O and P – are interviewed one after another in six consecutive slots.
N is interviewed before both K and O.
M is interviewed immediately after L.
K is interviewed after M.
O is not interviewed last.
Which of the following must be true?
Answer options for question 34 A N is interviewed first. B P is interviewed last. C O is interviewed before K. D K is interviewed in the fourth slot or later.
Question 35 Probabilistic reasoning A condition affects 1 in 50 people in a population. A screening test gives a positive result for 90% of people who have the condition, and also for 10% of people who do not have it.
A person chosen at random from the population tests positive. Approximately what is the probability that they have the condition?
Answer options for question 35 A 2% B 16% C 50% D 90%