UCAT — University Clinical Aptitude Test (UK medicine)

UCAT Quantitative Reasoning, Set 2

Take the UCAT Quantitative Reasoning, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20 UCAT…

What this test covers

20 UCAT Quantitative Reasoning

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. The graph shows average waiting times at two hospitals. In which quarter were the waiting times equal?
- A. Q2
- B. Q1
- C. Q4
- D. Q3 ✓
Answer: D. Q3
Explanation: Both hospitals had a 150-minute average in Q3.
Q2. Using the graph, by what percentage did Hospital A's average wait fall from Q1 to Q4?
- A. 18.0%
- B. 22.2% ✓
- C. 40%
- D. 28.6%
Answer: B. 22.2%
Explanation: (180 − 140)/180 = 0.222 = 22.2%.
Q3. Using the graph, what was Hospital B's mean waiting time over the four quarters?
- A. 150 minutes
- B. 145 minutes
- C. 143.75 minutes ✓
- D. 135 minutes
Answer: C. 143.75 minutes
Explanation: (120 + 135 + 150 + 170)/4 = 575/4 = 143.75.
Q4. Using the graph, how much longer was the average wait at Hospital B than at Hospital A in Q4?
- A. 40 minutes
- B. 30 minutes ✓
- C. 10 minutes
- D. 20 minutes
Answer: B. 30 minutes
Explanation: 170 − 140 = 30 minutes.
Q5. If Hospital A's wait keeps falling by the same amount as from Q3 to Q4, what will it be in the next quarter?
- A. 135 minutes
- B. 125 minutes
- C. 130 minutes ✓
- D. 140 minutes
Answer: C. 130 minutes
Explanation: It fell by 10 minutes from Q3 to Q4, so 140 − 10 = 130.

The other 15 questions

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Q6. The timetable shows trains from Northgate to Riverside. Which train has the shortest journey?
- A. The 08:05
- B. The 09:40
- C. The 11:10
- D. The 07:15
Q7. Using the timetable, what is the mean journey time of the four trains?
- A. 38 minutes
- B. 37.25 minutes
- C. 36.5 minutes
- D. 39.75 minutes
Q8. Using the timetable, what percentage is saved by travelling off-peak instead of peak?
- A. 26.2%
- B. 22.0%
- C. 18.6%
- D. 35.5%
Q9. A commuter takes the 08:05 train every weekday for one week (5 days), buying a single each time. How much does she spend?
- A. £42.00
- B. £31.00
- C. £84.00
- D. £40.00
Q10. A traveller must arrive in Riverside before 10:30 and wants the cheapest fare. Which train should they take?
- A. The 08:05
- B. The 09:40
- C. The 07:15
- D. The 11:10
Q11. A child's dose is 15 mg per kg. How much should a 22 kg child receive?
- A. 345 mg
- B. 37 mg
- C. 300 mg
- D. 330 mg
Q12. A nurse can complete 6 patient checks per hour. How many hours are needed for 45 checks?
- A. 6 hours
- B. 8 hours
- C. 7 hours
- D. 7.5 hours
Q13. A medicine's price rose from £12.50 to £15.00. What is the percentage increase?
- A. 2.5%
- B. 25%
- C. 20%
- D. 16.7%
Q14. A patient's weight is 72 kg. If 1 kg = 2.2 pounds, what is this in pounds?
- A. 158.4 pounds
- B. 74.2 pounds
- C. 32.7 pounds
- D. 144 pounds
Q15. A hospital has nurses and doctors in the ratio 5 : 2. There are 84 staff in total. How many are nurses?
- A. 42
- B. 70
- C. 24
- D. 60
Q16. A cyclist rides 24 km in 1 hour 20 minutes. What is the average speed?
- A. 24 km/h
- B. 16 km/h
- C. 20 km/h
- D. 18 km/h
Q17. A price is reduced by 20% and then increased by 25%. Compared with the original price, the final price is:
- A. The same
- B. 45% higher
- C. 5% higher
- D. 5% lower
Q18. Five patients waited 12, 18, 25, 30 and 15 minutes. What was the mean wait?
- A. 20 minutes
- B. 22 minutes
- C. 25 minutes
- D. 18 minutes
Q19. A medicine must be taken every 8 hours. The first dose is at 06:30. When is the third dose?
- A. 23:30
- B. 21:30
- C. 22:30
- D. 14:30
Q20. A conference costs €240. If £1 = €1.20, what is the cost in pounds?
- A. £192
- B. £200
- C. £220
- D. £288