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Civil Service Numerical Test study materials
Civil Service Numerical Test study resources

Civil Service Numerical Test practice questions

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Question 1Basic number operations and arithmetic fluency

What is 4,786 + 2,357?

  1. 7,143 Correct answer.
  2. 7,133
  3. 7,043
  4. 7,243

Explanation

Add column by column from the right: ones 6 + 7 = 13, so write 3 and carry 1; tens 8 + 5 + 1 = 14, write 4 and carry 1; hundreds 7 + 3 + 1 = 11, write 1 and carry 1; thousands 4 + 2 + 1 = 7. The total is therefore 7,143.

Question 2Basic number operations and arithmetic fluency

What is 9,002 − 3,468?

  1. 5,534 Correct answer.
  2. 5,434
  3. 5,634
  4. 5,524

Explanation

Borrow across the zeros: 9,002 becomes 8 thousands, 9 hundreds, 9 tens and 12 ones. Subtracting gives 5,534, which can be checked by adding 5,534 + 3,468 = 9,002.

Question 3Basic number operations and arithmetic fluency

What is 47 × 26?

  1. 1,122
  2. 1,222 Correct answer.
  3. 1,212
  4. 1,232

Explanation

Split the multiplication: 47 × 20 = 940 and 47 × 6 = 282. Adding the two partial products gives 940 + 282 = 1,222.

Question 4Basic number operations and arithmetic fluency

What is 936 ÷ 8?

  1. 116
  2. 107
  3. 127
  4. 117 Correct answer.

Explanation

Divide in stages: 936 ÷ 8 = (800 ÷ 8) + (136 ÷ 8) = 100 + 17 = 117. Checking by multiplication, 8 × 117 = 936, which confirms the answer.

Question 5Basic number operations and arithmetic fluency

What is 15% of 240?

  1. 40
  2. 24
  3. 36 Correct answer.
  4. 32

Explanation

Split the percentage: 10% of 240 is 24 and 5% is 12. Adding these parts gives 24 + 12 = 36, so 15% of 240 is 36.

Question 6Basic number operations and arithmetic fluency

What is 3/4 + 5/6?

  1. 8/10
  2. 1 5/12
  3. 1 7/12 Correct answer.
  4. 1 3/4

Explanation

Use the lowest common denominator, 12: 3/4 = 9/12 and 5/6 = 10/12. Adding gives 19/12, which as a mixed number is 1 7/12.

Question 7Basic number operations and arithmetic fluency

What is the value of 8 + 4 × 3 − 6 ÷ 2?

  1. 17 Correct answer.
  2. 21
  3. 15
  4. 14

Explanation

Multiplication and division are carried out before addition and subtraction: 4 × 3 = 12 and 6 ÷ 2 = 3. The expression becomes 8 + 12 − 3 = 17.

Question 8Basic number operations and arithmetic fluency

What is 0.6 × 0.45?

  1. 0.027
  2. 0.27 Correct answer.
  3. 0.30
  4. 2.7

Explanation

Multiply the digits: 6 × 45 = 270. The factors have 1 + 2 = 3 decimal places in total, so place the decimal point three places from the right to get 0.270, that is, 0.27.

Question 9Basic number operations and arithmetic fluency

What is 46,738 rounded to the nearest hundred?

  1. 47,000
  2. 46,740
  3. 46,700 Correct answer.
  4. 46,800

Explanation

To round to the nearest hundred, look at the tens digit. The tens digit is 3, which is less than 5, so the hundreds digit stays at 7 and the digits to its right become zeros, giving 46,700.

Question 10Basic number operations and arithmetic fluency

What is the mean of 12, 18, 9, 25 and 16?

  1. 15
  2. 17
  3. 18
  4. 16 Correct answer.

Explanation

The mean is the total divided by the number of values. The total is 12 + 18 + 9 + 25 + 16 = 80, and 80 ÷ 5 = 16.

Question 11Basic number operations and arithmetic fluency

A sum of 240 is shared in the ratio 3 : 5. How much is the larger share?

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

Explanation

The ratio 3 : 5 has 3 + 5 = 8 equal parts, so one part is 240 ÷ 8 = 30. The larger share is 5 parts, that is, 5 × 30 = 150.

Question 12Basic number operations and arithmetic fluency

What is the value of −7 + 12 − (−5)?

  1. −10
  2. 10 Correct answer.
  3. 14
  4. 0

Explanation

Subtracting a negative number is the same as adding its positive value, so the expression becomes −7 + 12 + 5. Working left to right: −7 + 12 = 5, then 5 + 5 = 10.

Question 13Basic number operations and arithmetic fluency

Which of these numbers is exactly divisible by 9?

  1. 4,536 Correct answer.
  2. 4,532
  3. 4,538
  4. 4,540

Explanation

A number is divisible by 9 when the sum of its digits is a multiple of 9. For 4,536 the digit sum is 4 + 5 + 3 + 6 = 18, which is a multiple of 9, so 4,536 is divisible by 9.

Question 14Basic number operations and arithmetic fluency

What is the lowest common multiple of 12 and 18?

  1. 216
  2. 6
  3. 36 Correct answer.
  4. 72

Explanation

Write each number in prime form: 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest power of each prime, giving 2² × 3² = 4 × 9 = 36, which is the smallest number both divide exactly.

Question 15Basic number operations and arithmetic fluency

A distance of 3.4 kilometres is equal to how many metres?

  1. 340
  2. 34,000
  3. 3,400 Correct answer.
  4. 3,040

Explanation

One kilometre contains 1,000 metres, so converting to metres means multiplying by 1,000. Moving the decimal point three places to the right gives 3.4 × 1,000 = 3,400 metres.

Question 16Basic number operations and arithmetic fluency

A price rises from 80 to 92. What is the percentage increase?

  1. 15% Correct answer.
  2. 10%
  3. 12%
  4. 20%

Explanation

Percentage increase is the increase divided by the original value, then multiplied by 100. The increase is 92 − 80 = 12, and 12 ÷ 80 = 0.15, which is 15%.

Question 17Basic number operations and arithmetic fluency

What is 2/5 of 350?

  1. 175
  2. 120
  3. 140 Correct answer.
  4. 210

Explanation

Find one fifth first: 350 ÷ 5 = 70. Then take two of those fifths: 2 × 70 = 140.

Question 18Basic number operations and arithmetic fluency

What is the value of (5 + 3)² ÷ 4 − 6 × 2?

  1. 28
  2. 10
  3. 16
  4. 4 Correct answer.

Explanation

Work out the brackets first: 5 + 3 = 8, and 8² = 64. Then handle division and multiplication: 64 ÷ 4 = 16 and 6 × 2 = 12. Finally subtract: 16 − 12 = 4.

Question 19Basic number operations and arithmetic fluency

What is 4.8 ÷ 0.06?

  1. 80 Correct answer.
  2. 0.8
  3. 800
  4. 8

Explanation

Multiply both numbers by 100 to remove the decimal from the divisor: 4.8 ÷ 0.06 becomes 480 ÷ 6. Since 6 × 80 = 480, the quotient is 80.

Question 20Basic number operations and arithmetic fluency

What is 3/8 written as a decimal?

  1. 0.375 Correct answer.
  2. 0.83
  3. 0.125
  4. 0.38

Explanation

A fraction is a division, so 3/8 means 3 ÷ 8. Dividing gives 0.375, since 8 × 0.375 = 3.

Question 21Basic number operations and arithmetic fluency

A sum of 2,500 earns simple interest at 4% per year for 3 years. How much interest is earned in total?

  1. 400
  2. 300 Correct answer.
  3. 100
  4. 250

Explanation

Simple interest is calculated as principal × rate × time. Here that is 2,500 × 0.04 × 3 = 300, so the total interest is 300.

Question 22Basic number operations and arithmetic fluency

Six workers can complete a task in 12 days, all working at the same steady rate. How long would eight workers take to complete the same task?

  1. 16
  2. 8
  3. 9 Correct answer.
  4. 10

Explanation

The task needs 6 × 12 = 72 worker-days of effort in total. With 8 workers the time is 72 ÷ 8 = 9 days, because more workers means proportionally fewer days.

Question 23Basic number operations and arithmetic fluency

What is the value of 0.25 + 3/4 × 8?

  1. 6.25 Correct answer.
  2. 6
  3. 6.75
  4. 8

Explanation

Multiplication is performed before addition, so first compute 3/4 × 8 = 6. Then add the 0.25 to obtain 6.25.

Question 24Basic number operations and arithmetic fluency

What is the value of (2⁵ − 3²) × 2?

  1. 14
  2. 23
  3. 32
  4. 46 Correct answer.

Explanation

Evaluate the powers first: 2⁵ = 32 and 3² = 9. The bracket becomes 32 − 9 = 23, and multiplying by 2 gives 46.

Question 25Basic number operations and arithmetic fluency

Which value is the best estimate of 497 × 21?

  1. 5,000
  2. 100,000
  3. 10,000 Correct answer.
  4. 1,000

Explanation

Round each factor to a convenient number: 497 is close to 500 and 21 is close to 20. Then 500 × 20 = 10,000, which is the closest estimate to the true product of 10,437.

Question 26Basic number operations and arithmetic fluency

In the number 4,738,215, what is the value of the digit 7?

  1. 700,000
  2. 70,000 Correct answer.
  3. 7,000
  4. 7,000,000

Explanation

In a whole number, each position is ten times the value of the position to its right. The 7 is in the ten-thousands place, so its value is 7 × 10,000 = 70,000.

Question 27Basic number operations and arithmetic fluency

A pack contains 24 pencils. How many pencils are there in 15 identical packs?

  1. 240
  2. 380
  3. 360 Correct answer.
  4. 340

Explanation

Multiply the number of pencils in one pack by the number of packs: 24 × 15. This equals 24 × 10 + 24 × 5 = 240 + 120 = 360.

Question 28Basic number operations and arithmetic fluency

What is the remainder when 437 is divided by 8?

  1. 3
  2. 7
  3. 4
  4. 5 Correct answer.

Explanation

Divide 437 by 8: 8 × 54 = 432, and 437 − 432 = 5. The remainder is 5.

Question 29Basic number operations and arithmetic fluency

Which of these numbers is a prime number?

  1. 51
  2. 57
  3. 59 Correct answer.
  4. 63

Explanation

A prime number has exactly two factors, 1 and itself. Testing primes up to about 7 shows that 59 has no divisor other than 1 and 59, so it is prime.

Question 30Basic number operations and arithmetic fluency

What is the value of (−3) × (−4) + (−6)?

  1. 6 Correct answer.
  2. −6
  3. −18
  4. 18

Explanation

The product of two negative numbers is positive, so (−3) × (−4) = 12. Adding −6 gives 12 − 6 = 6.

Question 31Basic number operations and arithmetic fluency

A recipe uses 2/3 cup of sugar for each batch. How many cups of sugar are needed for 4 1/2 batches?

  1. 3 Correct answer.
  2. 3 1/3
  3. 4
  4. 2

Explanation

Write 4 1/2 as 9/2, then multiply by 2/3 per batch: 2/3 × 9/2 = 18/6 = 3. Three cups are needed.

Question 32Basic number operations and arithmetic fluency

After a 15% discount, a jacket costs 68. What was its price before the discount?

  1. 78.20
  2. 102.00
  3. 80.00 Correct answer.
  4. 83.00

Explanation

After a 15% discount, the price paid is 85% of the original price. Divide 68 by 0.85: 68 ÷ 0.85 = 80.

Question 33Basic number operations and arithmetic fluency

What is 12.6 ÷ 3?

  1. 42
  2. 4.2 Correct answer.
  3. 4.02
  4. 0.42

Explanation

Dividing 12.6 by 3 gives 4.2 because 4.2 × 3 = 12.6. The decimal point stays in the correct place when the quotient is checked by multiplication.

Question 34Basic number operations and arithmetic fluency

What is the highest common factor of 36 and 60?

  1. 6
  2. 12 Correct answer.
  3. 24
  4. 18

Explanation

Write 36 = 2² × 3² and 60 = 2² × 3 × 5. The highest common factor uses the lowest power of each shared prime: 2² × 3 = 12.

Question 35Basic number operations and arithmetic fluency

The mean of five numbers is 14. Four of the numbers are 10, 12, 15 and 18. What is the fifth number?

  1. 13
  2. 19
  3. 15 Correct answer.
  4. 11

Explanation

The total of the five numbers is 14 × 5 = 70. The four given numbers add to 10 + 12 + 15 + 18 = 55, so the fifth number is 70 − 55 = 15.

Question 36Basic number operations and arithmetic fluency

Concrete is made by mixing sand and cement in the ratio 4 : 1. How many kilograms of cement are needed to make 45 kg of concrete?

  1. 40
  2. 9 Correct answer.
  3. 36
  4. 11.25

Explanation

The ratio 4 : 1 means there are 5 equal parts in total. Each part is 45 ÷ 5 = 9 kg, and cement is 1 part, so 9 kg of cement is needed.

Question 37Basic number operations and arithmetic fluency

How many millilitres are there in 2.75 litres?

  1. 275
  2. 27,500
  3. 0.275
  4. 2,750 Correct answer.

Explanation

One litre contains 1,000 millilitres. Multiply 2.75 by 1,000 by moving the decimal point three places to the right, giving 2,750 ml.

Question 38Basic number operations and arithmetic fluency

A price of 250 is increased by 20%, and the new price is then reduced by 10%. What is the final price?

  1. 275
  2. 260
  3. 270 Correct answer.
  4. 300

Explanation

First increase: 250 × 1.20 = 300. Then reduce the new price by 10%: 300 × 0.90 = 270. The 10% reduction applies to 300, not to the original 250.

Question 39Basic number operations and arithmetic fluency

What is 3/5 of 2/9 of 450?

  1. 120
  2. 30
  3. 90
  4. 60 Correct answer.

Explanation

First find 2/9 of 450, which is 450 ÷ 9 × 2 = 100. Then take 3/5 of 100, giving 60.

Question 40Basic number operations and arithmetic fluency

In a school the ratio of boys to girls is 5 : 3. If there are 24 more boys than girls, how many students are there altogether?

  1. 96 Correct answer.
  2. 144
  3. 120
  4. 72

Explanation

The difference between 5 parts and 3 parts is 2 parts, and these equal 24 students. So one part is 12, and the total is 8 parts × 12 = 96 students.

Question 41Data interpretation from tables, charts and graphs

Books borrowed from a town library were recorded as follows: Monday 120, Tuesday 95, Wednesday 140, Thursday 110 and Friday 135. What was the total number of books borrowed over the five days?

  1. 600 Correct answer.
  2. 560
  3. 580
  4. 620

Explanation

Add the five daily figures: 120 + 95 + 140 + 110 + 135 = 600. A total is found by summing every category in the table, with no day counted twice.

Question 42Data interpretation from tables, charts and graphs

A bar chart shows the number of units sold by four shops in one month: North 340, South 285, East 410 and West 365. How many more units did East sell than South?

  1. 145
  2. 115
  3. 130
  4. 125 Correct answer.

Explanation

Subtract the South figure from the East figure: 410 − 285 = 125. A 'how many more' comparison is a difference between the two bars concerned, not a total.

Question 43Data interpretation from tables, charts and graphs

In a transport survey of 400 commuters, 96 said they travelled to work by bus. What percentage of the commuters travelled by bus?

  1. 18%
  2. 24% Correct answer.
  3. 21%
  4. 22%

Explanation

Divide the part by the whole and multiply by 100: 96 ÷ 400 × 100 = 24%. A percentage share always takes the full total, here 400, as its denominator.

Question 44Data interpretation from tables, charts and graphs

A line graph shows club membership at the end of each year: 2018 = 250, 2019 = 300, 2020 = 270 and 2021 = 360. By how much did membership increase between the end of 2018 and the end of 2021?

  1. 110 Correct answer.
  2. 150
  3. 130
  4. 90

Explanation

Read the two end points from the line and subtract: 360 − 250 = 110. The dip in 2020 is irrelevant when only the first and last years are compared.

Question 45Data interpretation from tables, charts and graphs

Visitor numbers at a museum over five days were 210, 240, 180, 250 and 220. What was the mean daily number of visitors?

  1. 215
  2. 218
  3. 220 Correct answer.
  4. 230

Explanation

The five days total 1,100 visitors, and 1,100 ÷ 5 = 220. A mean always divides the grand total by the number of observations.

Question 46Data interpretation from tables, charts and graphs

A table shows 45 staff in Department A and 75 staff in Department B. Expressed in its simplest form, what is the ratio of Department A staff to Department B staff?

  1. 2:3
  2. 3:5 Correct answer.
  3. 5:8
  4. 4:7

Explanation

Both numbers divide exactly by their highest common factor of 15, giving 45 ÷ 15 = 3 and 75 ÷ 15 = 5, so the ratio is 3:5. A simplified ratio contains whole numbers with no common factor remaining.

Question 47Data interpretation from tables, charts and graphs

A pie chart represents 720 survey responses. The sector labelled 'Cycling' has an angle of 90°. How many respondents chose cycling?

  1. 90
  2. 180 Correct answer.
  3. 120
  4. 150

Explanation

A full pie chart is 360°, so a 90° sector is one quarter of the whole: 720 × 90 ÷ 360 = 180. Sector size is always proportional to its angle.

Question 48Data interpretation from tables, charts and graphs

A table gives monthly exports in thousands of units: January 48.5, February 52.0 and March 46.5. What was the total for the three months?

  1. 147.0 thousand units Correct answer.
  2. 147.5 thousand units
  3. 148.0 thousand units
  4. 145.5 thousand units

Explanation

Add the three monthly figures: 48.5 + 52.0 + 46.5 = 147.0 thousand units. Decimal points must be aligned when adding tabulated values.

Question 49Data interpretation from tables, charts and graphs

A company's revenue fell from 480 million to 420 million in one year. By what percentage did revenue fall?

  1. 14.3%
  2. 11.5%
  3. 10.0%
  4. 12.5% Correct answer.

Explanation

The fall is 60 million, and percentage change divides this by the original value: 60 ÷ 480 × 100 = 12.5%. The original figure, not the new one, is the correct denominator.

Question 50Data interpretation from tables, charts and graphs

After a 15% increase, a factory's weekly output is 460 units. What was the output before the increase?

  1. 400 units Correct answer.
  2. 391 units
  3. 414 units
  4. 405 units

Explanation

Divide the final figure by the multiplier 1.15, since 460 = original × 1.15, giving 460 ÷ 1.15 = 400 units. Reversing a percentage increase means dividing, not subtracting the percentage.