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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.

Read the first 6 Numerical Reasoning flashcards as text

  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?

    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.

  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?

    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.

  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?

    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.

  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?

    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.

  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?

    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.

  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?

    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.