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OACP: Numerical reasoning without a calculator

Times, distances, speeds, averages, percentages and rates in practical police-style problems, worked by hand.

  • 14 questions
  • Topic drill
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Numerical reasoning without a calculator · Question 1Score 0/0

A car travels at 90 km/h for 2 hours 20 minutes. How far does it go?

Study reference: OACP Certificate study notes (Oct 2026), Ch. 9 Numerical reasoning — practical arithmetic

All 14 questions in this test

Every question and its answer choices. The correct answers and explanations appear when you take the test above.

  1. A car travels at 90 km/h for 2 hours 20 minutes. How far does it go?

    1. 220 km
    2. 200 km
    3. 210 km
    4. 180 km

  2. An officer works from 06:45 to 15:15. How long is the shift?

    1. 8 hours 45 minutes
    2. 8 hours 30 minutes
    3. 9 hours 30 minutes
    4. 8 hours 15 minutes

  3. How long does it take to drive 45 km at 90 km/h?

    1. 45 minutes
    2. 50 minutes
    3. 30 minutes
    4. 20 minutes

  4. Three officers share 18 blocks of a door-to-door canvass equally. How many blocks does each cover?

    1. 6
    2. 5
    3. 8
    4. 9

  5. What is 25% of 120?

    1. 30
    2. 25
    3. 35
    4. 40

  6. A search starts at 22:50 and lasts 1 hour 25 minutes. When does it end?

    1. 00:15
    2. 00:25
    3. 00:05
    4. 23:15

  7. An event needs one officer for every 40 guests. How many officers are needed for 360 guests?

    1. 9
    2. 8
    3. 10
    4. 12

  8. A cruiser uses 12 L of fuel per 100 km. How much fuel does it use on a 250 km patrol?

    1. 30 L
    2. 25 L
    3. 24 L
    4. 36 L

  9. Radar records four cars at 52, 58, 61 and 49 km/h. What is their average speed?

    1. 55 km/h
    2. 54 km/h
    3. 56 km/h
    4. 58 km/h

  10. Each evidence bag can hold 0.6 kg. How many bags are needed for 7.2 kg of material?

    1. 10
    2. 11
    3. 14
    4. 12

  11. A crowd of 240 people is at a rally, and 3/8 of them leave. How many people remain?

    1. 150
    2. 90
    3. 160
    4. 120

  12. Calls to a district rose from 80 one month to 100 the next. What is the percent increase?

    1. 15%
    2. 30%
    3. 25%
    4. 20%

  13. A cruiser travels at 60 km/h for 30 minutes. How far does it go?

    1. 90 km
    2. 30 km
    3. 20 km
    4. 60 km

  14. Three bags of evidence weigh 12.5 kg, 8.75 kg and 6.25 kg. What is the total weight?

    1. 28.25 kg
    2. 26.5 kg
    3. 27.5 kg
    4. 27 kg

Numerical reasoning without a calculator: key rules to remember

Our summary of what the official handbook says on this topic, in our own words. Read it before or after the practice questions above, then check the original chapter. Read the official chapter ↗

Why practise numbers (our study notes)

  • Police work and many reasoning tests involve times, distances, speeds and simple counts; practise doing them by hand.

Numbers for police-style problems (our study notes)

  • Distance = speed × time; at 60 km/h a vehicle travels 1 km every minute.
  • Average = total ÷ number of items.
  • Percent of a number: 25% of 80 = 0.25 × 80 = 20.
  • Elapsed time: count to the next full hour, then add the remaining minutes.
  • Rates: if 3 officers cover 12 blocks, each covers 4 blocks at the same rate.
  • Ratio and proportion: keep units the same before comparing.
  • Estimate first, then check whether the chosen answer is reasonable.

Study the Numerical reasoning without a calculator rules as flashcards →

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