Free Civil Service Numerical Test Exam Flashcards

Time taken does not affect the score, and submitted answers cannot be revisited or skipped. The next question may become harder or easier as the test adapts; official guidance does not disclose a special first 5–10-item scoring rule. Check units, the requested denominator, and the calculation before submitting each answer. Complete the application by its deadline.

A percentile rank shows the percentage of candidates in your grade-level comparison group whose estimated ability you exceeded (e.g., 65th percentile beats 65% of the norm group, not 65% raw correct). Passing the grade's minimum standard allows banking, but recruiters may raise the campaign pass mark after the deadline once all applicant scores are reviewed.

The four grade groupings are: (1) AA/AO, (2) EO, (3) HEO/SEO, and (4) Grade 7 / Grade 6 / SCS 1. Only a passing score is banked, and it expires when any one of three events occurs: 6 months elapse, a new score benchmark is applied, or platform technical work affects banked scores.

Every bar chart, line graph, and pie chart on the CSNT is accompanied by an alternative data table containing the underlying figures, allowing you to cross-check visual readings against exact numbers. If you are shortlisted for interview, the hiring manager may require you to retake the test under supervised conditions to verify your score.

Multiply the table cell by 1,000 first: 4,250 × £1,000 = £4,250,000. Then add the grant: £4,250,000 + £850,000 = £5,100,000 (or £5.1 m). Adding 4,250 directly to 850,000 (£854,250) or scaling the grant to £8,500,000 (£12.75 m) are classic unit-header traps.

For a stated April–March financial year, Q1 is April–June, Q2 July–September, Q3 October–December and Q4 January–March. If a problem specifies 52 paid weeks, annual cost equals weekly cost×52; using 4×12 counts only 48 weeks. Follow the table’s actual dates and payment schedule rather than assuming every annual payment problem uses exactly 52 weeks.

Headcount counts people; FTE divides contracted hours by the stated full-time baseline. If full time is 37 hours, one 37-hour worker and two 18.5-hour workers give headcount 3 and FTE=(37+18.5+18.5)/37=2. Use the baseline in the problem; 37 hours is this example’s assumption, not a universal rule.

The phrase immediately following 'of' or 'among' sets the denominator. 'What percentage of North West claims were upheld?' divides (North West upheld) by the North West row total. 'What percentage of all claims were upheld North West claims?' divides the same cell by the table's grand total.

Subtract the segment's bottom boundary from its top boundary: Segment Value = Top Reading - Bottom Reading. For example, if Direct Entry runs from 0 to 630 and Fast Stream stacks on top from 630 to 945, Fast Stream = 945 - 630 = 315, and its share of total intake is (315 / 945) × 100% ≈ 33.33%.

Visual height above the £420 m baseline: Dept A = 460 - 420 = 40 units; Dept B = 540 - 420 = 120 units, so Dept B looks 120 / 40 = 3.0 times taller. True percentage premium = ((540 - 460) / 460) × 100% = (80 / 460) × 100% ≈ 17.39% (approx. 17.4%). Always read axis numbers rather than visual bar proportions.

Absolute rate of change (gradient) = (Y 2 - Y 1) / (X 2 - X 1), expressed in units per time period (e.g., backlog falling from 23,000 to 18,000 over a 3-month quarter = -5,000 / 3 ≈ -1,667 cases/month). Relative percentage change = ((Y 2 - Y 1) / Y 1) × 100%, which measures proportional change from the starting value.

With no other adjustments: closing backlog=opening backlog+receipts−clearances. Starting at 100 cases, receipts/clearances of 40/30, 20/35, and 30/25 produce backlogs 110, 95, and 100. The maximum recorded closing backlog is 110 after period 1. A visual crossover in a graph does not alone identify the global maximum; calculate cumulative balances and account for transfers or other adjustments.

1% of a circle = 3.6° (since 360° / 100 = 3.6°). Angle = Percentage × 3.6°; Percentage = Angle / 3.6°; Value = (Angle / 360°) × Total Budget. Core benchmarks: 180° = 50%, 120° ≈ 33.33%, 90° = 25%, 72° = 20%, 60° ≈ 16.67%, 54° = 15%, 45° = 12.5%, 36° = 10%.

A smaller percentage slice in Year 2 can represent more actual money if the total budget grew. Example: Cloud spend is 35% of a £60 m budget in Year 1 (0.35 × £60 m = £21.0 m) and drops to 25% of a £96 m budget in Year 2 (0.25 × £96 m = £24.0 m). Despite a 10 percentage-point drop in share, cash spend rose by £3.0 m (+14.3%).

Follow each allowance’s stated base. If a 140-hour allowance loses 10% to admin, then 5% of the remaining hours to absence, productive time is 140×0.90×0.95=119.7 hours. If both deductions instead apply to gross hours, it is 140×(1−0.10−0.05)=119 hours. These are different assumptions, not competing arithmetic rules.

1) Convert each tier's minutes to decimal hours (Minutes / 60). 2) Sum (Tier Volume × Tier Hours) plus any required backlog clearance hours to get Total Demand Hours. 3) Divide Total Demand Hours by Net Productive Hours per FTE: Required FTE = Total Demand Hours / Net Hours per FTE.

If variance is defined as actual minus budget, calculate (Actual−Budget)/Budget×100% for a nonzero budget. In a simple cost-control table, overspend is adverse and underspend favourable; for income, exceeding target is favourable. Check the table’s sign convention and performance context—an underspend alone does not prove services were delivered successfully.

Not for judging compliance with those separate limits. If operating is £2 m over budget and capital is £3 m under, the combined arithmetic balance is £1 m under, but the operating limit is still breached unless a permitted transfer is authorized. Use the conditions stated in the problem rather than assuming all funds are interchangeable.

Suppose cost is Red when absolute variance exceeds 5.0%. Budget £35.00 m and actual £36.82 m give 1.82/35×100=5.2%, so Red. If an on-time rate is Amber from 90.0% inclusive to 95.0% exclusive, 746,200/820,000×100=91.0%, so Amber. Evaluate the unrounded result against the defined inclusive/exclusive limits.

Index_t = (Value_t / Value_Base) × 100, for an index with its base set to 100.0. Because the base is 100, the percentage change from the base period to period t is simply Index_t - 100 (e.g., an index of 124.6 means a +24.6% increase since the base year).

Never subtract the two index numbers and call the difference a percentage! 134.4 - 112.0 = 22.4 index points, NOT 22.4%. When neither period is the base year (100), divide the index point change by the starting index: ((134.4 - 112.0) / 112.0) × 100% = (22.4 / 112.0) × 100% = +20.0%.

Real Expenditure = (Nominal Expenditure / Price Index) × 100. Example: If 2024 nominal spend is £66.0 m and the 2024 GDP Deflator Index is 120.0 (Base 2020 = 100.0), real spend in 2020 prices is (£66.0 m / 120.0) × 100 = £55.0 m. If 2020 spend was £58.0 m, real purchasing power fell by £3.0 m (-5.17%) despite £8.0 m nominal growth.

1/8=0.125=12.5%; 3/8=0.375=37.5%; 5/8=0.625=62.5%; 7/8=0.875=87.5% are exact. 1/6=0.1666…≈16.67% and 1/12=0.08333…≈8.33% recur. Keep full precision until the requested final rounding; an approximate benchmark is useful for checking, not an exact substitution.

Percentage Change = ((New Value - Original Value) / Original Value) × 100%. A common distractor divides the change by the New Value instead of the Original Value. Example: Cases rising from 1,250 to 1,500 increase by (250 / 1,250) × 100% = 20.0% (dividing 250 by 1,500 gives the 16.7% trap).

Percentage Points (pp) = New Rate (%) - Old Rate (%) (simple subtraction). Relative Percentage Change (%) = ((New Rate - Old Rate) / Old Rate) × 100%. If a survey score rises from 40% to 50%, that is a +10.0 percentage-point increase, which equals a ((50 - 40) / 40) × 100% = +25.0% relative increase.

For a positive starting rate, relative change=(new−old)/old×100%. A fall from 8% to 6% is −2 percentage points and −25% relative change. For a nonzero shift and a starting rate between 0% and 100%, the numerical magnitude of the relative percentage is greater than the percentage-point shift. At a zero starting rate this relative-change formula is undefined.

Apply successive multipliers: 0.80×1.20=0.96, a 4% net decrease. A £500,000 budget becomes £480,000. For equal nonzero rates r on successive bases, (1−r)(1+r)=1−r², so they do not cancel. The second change applies to the changed value, not the original amount.

Divide the final post-change value by the decimal multiplier: Original = Final / (1 + r) for an increase, or Original = Final / (1 - r) for a decrease. Example: If a travel budget is £187,000 after a 15% cut, Original = £187,000 / 0.85 = £220,000. Never add 15% of £187,000 (£215,050), because the 15% cut applied to the larger original base. A 100% decrease has a zero multiplier, so the original cannot be recovered from the final zero alone.

To reverse a change of r, compute 1 / (1 + r) - 1. For a +25% increase (multiplier 1.25 = 5/4), the reverse multiplier is 4/5 = 0.80, requiring a 20% decrease. For a -20% discount (multiplier 0.80 = 4/5), the reverse multiplier is 5/4 = 1.25, requiring a 25% increase.

With 20% VAT, Gross = 1.20 × Net = (6/5) × Net. Therefore: Net Price = Gross / 1.20 (or Gross × 5/6), and VAT Amount = Gross / 6. Example: On a £144,000 VAT-inclusive invoice, VAT = £144,000 / 6 = £24,000 and Net = £120,000. Taking 20% of the gross (£28,800) is a classic error.

Remove the stated VAT: 1,056,000/1.20=£880,000. Reverse the discount: 880,000/0.88=£1,000,000. The discount excluding VAT is £120,000. State the tax basis; this arithmetic alone does not establish a taxpayer’s final saving or whether the purchaser can recover VAT.

Simple interest grows linearly on the original principal only: A = P(1 + r·t). Compound interest grows exponentially on principal plus accumulated interest: A = P(1 + r)^t. Example: £250,000 at 4% for 3 years yields £250,000 × (1 + 0.12) = £280,000 under simple interest, but £250,000 × (1.04)^3 = £281,216 under compound growth.

In a ratio A : B, the total number of parts is A + B, so Group A's share of the whole is A / (A + B), not A / B (e.g., 1 : 3 means 1 / (1 + 3) = 25% and 75%). Before simplifying a mixed-unit ratio, convert both sides to the same smaller unit (e.g., 450 g : 1.2 kg = 450 g : 1,200 g; divide by HCF 150 to get 3 : 8).

Divide the known pound/case figure by the exact number of ratio parts it represents to find 1 part, then multiply by the target parts. Example: If Alpha and Beta split files in the ratio 7 : 5 and Alpha receives 360 more files than Beta, the difference is 7 - 5 = 2 parts = 360, so 1 part = 180 and the total (12 parts) is 12 × 180 = 2,160 files.

Identify the shared bridge term (B) and scale both ratios so B equals their Lowest Common Multiple (LCM of 3 and 4 is 12). Multiply A : B by 4 to get 8 : 12, and multiply B : C by 3 to get 12 : 15. Merge them into the unified ratio A : B : C = 8 : 12 : 15 (total = 35 parts).

Assume fixed work, identical constant worker productivity, no new arrivals and no coordination losses. Then workers×days is constant. If 9 workers take 16 days, the work is 144 worker-days; 12 workers need 12 days. Without those assumptions, extra staff need not reduce completion time in exactly the inverse ratio.

At constant productivity, output per worker-hour is O/(W×D×H); its reciprocal is worker-hours per output unit. Twelve analysts×10 days×7 hours=840 worker-hours. If they audit 840 contracts, the rate is 1 contract per worker-hour. At the same rate, 15×14×8=1,680 worker-hours produce 1,680 contracts.

If 1 cm on a map equals k km on the ground, lengths multiply by k, but areas multiply by k². Example: At a scale of 1 : 40,000, 1 cm = 400 m = 0.4 km (k = 0.4 km/cm), so 1 cm² = (0.4 km)² = 0.16 km². A 15 cm² plot covers 15 × 0.16 = 2.40 km² (multiplying 15 by 0.4 to get 6.0 km² is the linear-scaling trap).

For durations in weeks of 2, 4, 4, 8, 12, 16, 96, replace 96 with 19. The mean falls by (96−19)/7=11 weeks. The median stays 8 and mode stays 4 because their positions/frequencies are unchanged. The range falls from 94 to 17. A different replacement could change the ordering or mode; resistance to outliers is not absolute immunity.

Missing Value = (Target Mean × Total Count n) - Sum of Known Values. Example: Five teams score 74%, 81%, 68%, 85%, and 77% (sum = 385). To achieve a 78% mean across all 6 teams, the required total is 78 × 6 = 468, so the 6th team must score 468 - 385 = 83%.

Weight each percentage by its actual denominator. If all 1,000 respondents in group A yield 80% satisfaction and all 200 respondents in group B yield 50%, satisfied counts are 800 and 100. Combined satisfaction=900/1,200=75%, not (80+50)/2=65%. Staff headcount is unsuitable as a weight if the percentages are based on different response counts.

1) Find the midpoint (m_i) of each interval by averaging its lower and upper bounds. 2) Multiply each midpoint by its frequency (f_i). 3) Divide the sum of those products by total frequency: Estimated Mean = ∑(f_i × m_i) / ∑f_i. This midpoint method is an estimate; an open-ended interval needs an additional stated assumption.

Convert minutes to hours: 2 hours 24 minutes=2+24/60=2.4 hours. Average speed is total distance/total time. For 120 miles at 60 mph and 120 miles at 40 mph, time is 2+3=5 hours, so 240/5=48 mph. The simple average 50 mph is wrong here because durations differ; equal-time legs would permit an unweighted speed average.

If two workers can work simultaneously at constant independent rates on the same divisible task, add 1/T_A+1/T_B. Times 10 and 15 hours alone give rate 1/6 task/hour, so 6 hours together. For staffing, divide required work by productive capacity and round up only when whole people are required. Bottlenecks, shared equipment and indivisible steps can invalidate simple rate addition.

Under the stated additive rule, 1,000+3×120=1,360 cases. If growth were 12% of the current level each month instead, 1,000×1.12³≈1,404.928 cases before rounding. Read the declared forecast rule; a short run of observed data does not uniquely determine future growth.

A table gives quarterly costs of £14 k, £18 k, unknown, and £21 k, with annual total £80 k. Known costs total £53 k, so the missing quarter is £27 k. Check that all four quarters share the same units and that the annual figure is a sum, not an average or cumulative entry. Do not infer an unstated pattern from neighboring values.

For Base/Quote = R: multiply by R to convert Base (GBP) to Quote (USD); divide by R to convert Quote (USD) to Base (GBP). Dealer quotes are from the bank's perspective: when a department sells GBP to buy USD, the bank buys Base (GBP) at the lower Bid rate (1.2820); when converting USD back into GBP, the bank sells Base (GBP) at the higher Ask rate (1.2860).

1) Implied cross-rate: EUR/NOK = (GBP/NOK) / (GBP/EUR) (e.g., 13.80 / 1.15 = 12.00 NOK per EUR). 2) Currency asymmetry: if Currency A appreciates by proportion p against Currency B, Currency B depreciates against A by d = p / (1 + p). Thus, if GBP appreciates by +25% (0.25) against USD, USD depreciates by 0.25 / 1.25 = 20.0%, not 25.0%.

Write one equation for total headcount (f + a = N) and one for total cost (c_f·f + c_a·a = Budget), then substitute f = N - a. Example: 60 analysts trained for £34,000 across Foundation (£400) and Advanced (£900) courses gives 400(60 - a) + 900 a = 34,000 -> 24,000 + 500 a = 34,000 -> 500 a = 10,000 -> a = 20 Advanced (and 40 Foundation).

Use ceiling rounding (always UP) for logistical capacity, safety ratios, and sealed batch orders so no person or item is left unserviced (e.g., 345 archive boxes in 24-box containers = 345 / 24 = 14.375 -> 15 containers). Use floor rounding (always DOWN) for fixed cash budgets and headcount caps so statutory limits are never breached (e.g., £48,000 grant / £550 per laptop ≈ 87.27 -> 87 laptops, leaving £150 unspent).