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Numerical Reasoning Flashcards

6 cards from real FAST STREAM practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  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?

    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.

  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?

    Answer: 11.5%

    Percentage increase = ((1.45 - 1.3) / 1.3) × 100 = (0.15 / 1.3) × 100 = 11.538...% ≈ 11.5%.

  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?

    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.

  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?

    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.

  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:

    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).

  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?

    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.