Quantitative Reasoning

A train travels from City A to City B, a distance of 240 km, at an average speed of 80 km/h. How long does the journey take?

• A2 hours
• B3 hours✓
• C4 hours
• D2.5 hours

Answer: Time = Distance / Speed = 240 / 80 = 3 hours.

A doctor earns £85,000 per year. After paying 40% income tax on earnings above £50,000 and 20% on the first £50,000, what is their net annual income?

• A£51,000
• B£57,000
• C£61,000✓
• D£63,000

Answer: Tax on first £50,000: 20% = £10,000. Tax on remaining £35,000: 40% = £14,000. Total tax = £24,000. Net = £85,000 - £24,000 = £61,000.

A clinical trial has 480 participants. 60% are assigned to the treatment group and the remainder to placebo. Of the treatment group, 75% show improvement. How many participants from the treatment group showed improvement?

• A180
• B216✓
• C240
• D270

Answer: Treatment group: 60% of 480 = 288. Improvement: 75% of 288 = 216.

A hospital ward has 32 beds. Currently 75% are occupied. If 4 more patients are admitted, what percentage of beds will be occupied?

• A81.25%
• B85.5%
• C87.5%✓
• D90%

Answer: Currently occupied: 75% of 32 = 24 beds. After 4 more: 28 occupied out of 32. 28/32 × 100 = 87.5%.

A patient's BMI is calculated as weight (kg) divided by height squared (m²). A patient weighs 80 kg and is 1.6 m tall. What is their BMI?

• A28.5
• B30.0
• C31.25✓
• D32.0

Answer: BMI = 80 / (1.6²) = 80 / 2.56 = 31.25.

A medication must be dosed at 5 mg per kg of body weight. A patient weighs 68 kg. The medication comes in 20 mg tablets. How many tablets are needed?

• A15
• B16
• C17✓
• D18

Answer: Dose needed: 5 × 68 = 340 mg. Tablets: 340 / 20 = 17 tablets.

A study finds that a new drug reduces recovery time from 10 days to 7 days on average. What is the percentage reduction in recovery time?

• A25%
• B28%
• C30%✓
• D33%

Answer: Reduction = (10 - 7) / 10 × 100 = 3/10 × 100 = 30%.

A hospital spends £2.4 million on staffing, which represents 60% of its total annual budget. What is the total annual budget?

• A£3.6 million
• B£3.8 million
• C£4.0 million✓
• D£4.2 million

Answer: If £2.4M = 60%, then total = £2.4M / 0.6 = £4.0 million.

Blood pressure readings are recorded for 5 patients: 120, 135, 118, 142, 130 mmHg. What is the mean blood pressure?

• A127 mmHg
• B129 mmHg✓
• C131 mmHg
• D130 mmHg

Answer: Mean = (120 + 135 + 118 + 142 + 130) / 5 = 645 / 5 = 129 mmHg.

A GP practice sees 240 patients per week. Due to a new booking system, the number of patients seen increases by 15%. How many patients are seen per week after the change?

• A264
• B270
• C276✓
• D280

Answer: Increase: 15% of 240 = 36. New total: 240 + 36 = 276.

An IV drip delivers medication at 40 ml per hour. A bag contains 500 ml. After how many hours and minutes will the bag be empty?

• A12 hours 00 minutes
• B12 hours 15 minutes
• C12 hours 30 minutes✓
• D12 hours 45 minutes

Answer: 500 / 40 = 12.5 hours = 12 hours and 30 minutes.

In a cohort of 1000 people, 200 are smokers. The incidence of lung cancer in smokers is 8% and in non-smokers is 1%. How many people in total are expected to develop lung cancer?

• A24✓
• B28
• C32
• D16

Answer: Smokers with cancer: 8% of 200 = 16. Non-smokers with cancer: 1% of 800 = 8. Total = 16 + 8 = 24.