Fast Stream Numerical Reasoning — Questions and Answers
Question 1: A government department's budget was £240 million in 2022/23. It received a 5% increase for 2023/24, but then faced a 3% real-terms cut for 2024/25. What was the department's budget for 2024/25?
- £244.44 million (Correct answer)
- £244.78 million
- £252.00 million
- £247.80 million
Correct answer: £244.44 million
First, apply the 5% increase: £240m × 1.05 = £252m. Then apply the 3% cut: £252m × 0.97 = £244.44m. The increases and decreases must be applied sequentially, not netted off.
Question 2: A Civil Service diversity report shows that 48% of applicants to the Fast Stream were female, and 52% were male. If 12% of female applicants and 10% of male applicants were successful, and there were 25,000 total applicants, what was the total number of successful candidates?
- 2,740 (Correct answer)
- 2,700
- 2,500
- 2,800
Correct answer: 2,740
Female applicants: 25,000 × 0.48 = 12,000. Successful females: 12,000 × 0.12 = 1,440. Male applicants: 25,000 × 0.52 = 13,000. Successful males: 13,000 × 0.10 = 1,300. Total successful: 1,440 + 1,300 = 2,740.
Question 3: A local authority collects council tax from 45,000 households. The average Band D rate is £1,820 per year. If the collection rate is 96.5%, how much council tax revenue does the authority actually collect?
- £79,033,500 (Correct answer)
- £81,900,000
- £78,975,000
- £81,000,000
Correct answer: £79,033,500
Total potential revenue: 45,000 × £1,820 = £81,900,000. Actual collection at 96.5%: £81,900,000 × 0.965 = £79,033,500.
Question 4: A policy team analyses NHS waiting times. In Quarter 1, the average wait was 18 weeks. In Quarter 2 it rose by 15%, and in Quarter 3 it fell by 10% from the Quarter 2 figure. What was the average waiting time in Quarter 3, rounded to one decimal place?
- 18.6 weeks (Correct answer)
- 18.9 weeks
- 18.0 weeks
- 18.3 weeks
Correct answer: 18.6 weeks
Q1: 18 weeks. Q2: 18 × 1.15 = 20.7 weeks. Q3: 20.7 × 0.90 = 18.63 weeks, which rounds to 18.6 weeks. Note that a 15% increase followed by a 10% decrease does not return to the original value.
Question 5: The UK government spent £55.3 billion on education in 2022/23. If this represented 4.2% of GDP, what was the approximate GDP?
- £1,317 billion (Correct answer)
- £1,250 billion
- £1,400 billion
- £1,150 billion
Correct answer: £1,317 billion
If £55.3 billion = 4.2% of GDP, then GDP = £55.3bn ÷ 0.042 = £1,316.67 billion, approximately £1,317 billion.
Question 6: A department needs to reduce its headcount by 12% from 8,500 staff over three years, with equal reductions each year. How many staff should remain at the end of Year 1?
- 8,160 (Correct answer)
- 7,480
- 8,000
- 7,820
Correct answer: 8,160
Total reduction: 8,500 × 0.12 = 1,020 staff. Annual reduction: 1,020 ÷ 3 = 340 staff per year. After Year 1: 8,500 - 340 = 8,160 staff.
Fast Stream Numerical Reasoning
A government department's budget was £240 million in 2022/23.
It received a 5% increase for 2023/24, but then faced a 3% real-terms cut for 2024/25.
What was the department's budget for 2024/25?