Fast Stream Numerical Reasoning 2 — Questions and Answers
Question 1: A government procurement team receives bids from three suppliers. Supplier A quotes £2.4m with a 95% quality score. Supplier B quotes £2.1m with an 88% quality score. Supplier C quotes £2.7m with a 98% quality score. Using a weighted evaluation of 60% quality and 40% price (where lowest price scores 100%), which supplier scores highest overall?
- Supplier A
- Supplier B (Correct answer)
- Supplier C
- Suppliers A and C are tied
Correct answer: Supplier B
Price scores (lowest £2.1m = 100%): A = (2.1/2.4) × 100 = 87.5%, B = 100%, C = (2.1/2.7) × 100 = 77.8%. Weighted: A = (0.6 × 95) + (0.4 × 87.5) = 92.0. B = (0.6 × 88) + (0.4 × 100) = 92.8. C = (0.6 × 98) + (0.4 × 77.8) = 89.9. Supplier B scores highest at 92.8.
Question 2: UK unemployment was 1.3 million in January 2023. By January 2024, it had risen to 1.45 million. What was the percentage increase, to one decimal place?
- 11.5% (Correct answer)
- 10.3%
- 15.0%
- 12.8%
Correct answer: 11.5%
Percentage increase = ((1.45 - 1.3) / 1.3) × 100 = (0.15 / 1.3) × 100 = 11.538...% ≈ 11.5%.
Question 3: A policy team models the impact of a proposed tax. They estimate it would raise £3.2 billion annually but reduce consumer spending by £1.8 billion, which would decrease VAT revenue by 20% of that spending reduction. What is the net revenue gain?
- £2.84 billion (Correct answer)
- £1.40 billion
- £3.20 billion
- £2.56 billion
Correct answer: £2.84 billion
New tax revenue: £3.2bn. Lost VAT revenue: 20% of £1.8bn = £0.36bn. Net revenue gain: £3.2bn - £0.36bn = £2.84bn. The £1.8bn spending reduction itself is not a government revenue loss — only the VAT portion (20%) represents lost tax revenue.
Question 4: A Civil Service workforce survey shows 62% of respondents are satisfied with their role. If the survey had 15,400 respondents and a margin of error of ±2.5%, what is the range of the estimated number of satisfied staff?
- 9,163 to 9,933 (Correct answer)
- 9,000 to 10,000
- 8,500 to 10,500
- 9,240 to 9,856
Correct answer: 9,163 to 9,933
Lower bound: (62% - 2.5%) × 15,400 = 59.5% × 15,400 = 9,163. Upper bound: (62% + 2.5%) × 15,400 = 64.5% × 15,400 = 9,933. The range is 9,163 to 9,933.
Question 5: Three government projects have the following cost-benefit ratios: Project X has benefits of £45m against costs of £30m, Project Y has benefits of £28m against costs of £14m, and Project Z has benefits of £60m against costs of £35m. Ranked by benefit-cost ratio from highest to lowest, the order is:
- Y, Z, X (Correct answer)
- Z, X, Y
- X, Y, Z
- Y, X, Z
Correct answer: Y, Z, X
Calculate each ratio: X = £45m ÷ £30m = 1.50, Y = £28m ÷ £14m = 2.00, Z = £60m ÷ £35m = 1.71. Ranked highest to lowest: Y (2.00), Z (1.71), X (1.50).
Question 6: A department processes 2,400 Freedom of Information requests per year. They must respond within 20 working days. If 78% are answered on time and the department wants to improve this to 92%, how many additional requests per year need to be answered on time?
- 336 (Correct answer)
- 288
- 408
- 312
Correct answer: 336
Currently on time: 2,400 × 0.78 = 1,872. Target on time: 2,400 × 0.92 = 2,208. Additional needed: 2,208 - 1,872 = 336.
Fast Stream Numerical Reasoning 2
A government procurement team receives bids from three suppliers.
Supplier A quotes £2.4m with a 95% quality score.
Supplier B quotes £2.1m with an 88% quality score.
Supplier C quotes £2.7m with a 98% quality score.
Using a weighted evaluation of 60% quality and 40% price (where lowest price scores 100%), which supplier scores highest overall?